Introduction to Trigonometry

CBSE Class 10 Mathematics · every board question from this chapter, 2022–2026

• Given cot θ=3, the value of cos θ is:2026
• For an acute angle θ, if cos θ=1/8, then (8 sec θ+1)/(8 sec θ-1) equals2026
• Given that sin θ=a/b, then cos θ is equal to:2026
• (sec^2 A-1)/(sin^2 A) is same as2026
• If cos A=1/2, then the value of sin^2 A+2 cos^2 A is:2026
• If cos y=0, then what is the value of 1/2 cos y/2?2026
• If cos A=4/5, then the value of tan A is:2026
• When sin A=1/3, the value of cot A is2026
• If 2 sin A=1, then the value of tan A+ cot A is:2026
• The value of (1/3 cot^2 30^°-1/2 sec^2 60^°) is:2026
• (1+ tan^2 A)/(1+ cot^2 A) equals to:2026
• An arc of length 2.2 cm subtends an angle θ at the centre of the circle with radius 2.8 cm. The value of θ is2026
• For an acute angle θ, if sin θ=1/9, then value of (9 cosec θ+1)/(9 cosec θ-1) is2026
• Given that sin 2 α=(√3)/2, the value of sin 3 α is:2026
• Area of a segment of a circle of radius ' r ' and central angle 60^° is:2026
• The hour hand of a clock is 7 cm long. The angle swept by it between 7:00 a.m. and 8:10 a.m. is:2026
• If 2 tan A=3, then value of sec A equals2026
• The distance between the points (a cos θ+b sin θ, 0) and (0, a sin θ-b cos θ) is2026
• Arc PQ subtends an angle θ at the centre of the circle with radius 6.3 cm. If PQ=11 cm, then the value of θ is2026
• The value of (1/2 tan^2 45^°- cos^2 60^°) is:2026
• Simplest form of (sec A)/(√(sec^2 A-1)) is2026
• Assertion: tan 2 θ is not defined at θ=45^°. Reason (R): sin 90^° ≠ cos 90^°.2026
• Prove that: (tan θ)/(1+ tan^2 θ)+(cot θ)/(1+ cot^2 θ)=2 sin θ cos θ. OR Evaluate: (1-2 tan^2 30^°- sec^2 45^°)/(sin^2 60^°)2026
• Evaluate: (5 cos^2 60^°+4 sec^2 30^°- tan^2 45^°)/(sin^2 30^°+ cos^2 30^°) OR Prove that: 1+(cot^2 α)/(1+cosec α)=cosec α2026
• For acute angles A and B, if sec (2 A-B)=√2 and cosec(A+B)=2, then find the values of A and B. OR Evaluate: (2 cos 30^°- cot^3…2026
• Vertices of a right triangle ABC with ∠ B=90^° are A(3,4), B(1,1) and C(-8, 7). Find the value of tan A. OR Using distance…2026
• If tan θ=24/7, then find the value of sin θ+ cos θ. If cot θ=7/8, then find the value of ((1+ sin θ)(1- sin θ))/((1+ cos θ)(1-…2026
• Prove that: √((1+ sin A)/(1- sin A))= sec A+ tan A OR Evaluate: (3 cos^2 30^°-6 cosec^2 30^°)/(tan^2 60^°)2026
• If tan θ+1/(tan θ)=2, find the value of tan^2 θ+1/(tan^2 θ). OR Prove that: √((1- sin θ)/(1+ sin θ))= sec θ- tan θ2026
• Evaluate: (sin^3 60^°- tan 30^°)/(cos^2 45^°) OR For acute angles A and B and A + 2B and 2A + B are acute if tan (A+2 B)=√3 and…2026
• If tan θ=24/7, then find the value of sin θ+ cos θ. OR If cot θ=7/8, then find the value of ((1+ sin θ)(1- sin θ))/((1+ cos θ)(1-…2026
• If tan A=4/3, find sin A and cos A. OR Express cos A and tan A in terms of sin A.2026
• If sin θ+ cos θ=√3, then prove that tan θ+ cot θ=1 OR Prove that: ( sin A+ sec A)^2+( cos A+cosec A)^2=(1+ sec A cosec A)^22026
• Prove that: (tan θ)/(1- cot θ)+(cot θ)/(1- tan θ)=1+ tan θ+ cot θ.2026
• Prove that: (sec^3 θ)/(sec^2 θ-1)+(cosec^3 θ)/(cosec^2 θ-1)= sec θ · cosec θ( sec θ+cosec θ) OR If (sec α)/(cosec β)=p and (tan…2026
• If x=h+a cos θ, y=k+b sin θ, then prove that: ((x-h)/a)^2+((y-k)/b)^2=1 OR Prove that: (tan A)/(1+ sec A)-(tan A)/(1- sec A)=2…2026
• Prove that: (sin θ- cos θ+1)/(sin θ+ cos θ-1)=1/(sec θ- tan θ)2026
• Prove that: 1/(sec x- tan x)-1/(cos x)=1/(cos x)-1/(sec x+ tan x)2026
• Prove that: (1+ cot θ-cosec θ)(1+ tan θ+ sec θ)=22026
• The perimeter of sector OAB of a circle with centre O and radius 5.6 cm, is 15.6 cm. Find length of the arc AB. Also find the…2026
• If sec θ+ tan θ=m, show that (m^2-1)/(m^2+1)= sin θ.2026
• In a class test, the sum of Anamika's marks obtained in Maths and Science is 30. Had she got 2 marks more in Maths and 3 marks…2026
• Carom board is a very popular game. The board is a square of side length 65 cm. It has circular pockets in each corner. Ansh…2026
• Carom board is a very popular game. The board is a square of side length 65 cm. It has circular pockets in each corner. Ansh…2026
• If tan 3 θ=√3, then (θ)/2 equals:2025
• If 7 cos^2 θ+3 sin^2 θ=4, then the value of θ is:2025
• The value of ( tan A cosec A)^2-( sin A sec A)^2 is:2025
• If sin θ= cos θ(0^°<θ<90^°), then the value of sec θ · sin θ is:2025
• The value of (1-2 sin^2 60^°) is same as that of2025
• If x=2 sin 60^° cos 60^° and y= sin^2 30^°- cos^2 30^° and x^2=ky^2, the value of k is2025
• If θ is an acute angle and 7+4 sin θ=9, then the value of θ is:2025
• If sin 4 θ=(√3)/2, then (θ)/3 equals:2025
• The value of tan^2 θ-(1/(cos θ) × sec θ) is:2025
• If α+β=90^° and α=2 β, then cos^2 α+ sin^2 β is equal to:2025
• tan 2 A=3 tan A is true, when the measure of ∠ A is:2025
• ( cot θ+ tan θ) equals:2025
• Which of the following statements is true?2025
• Which of the following is a trigonometric identity?2025
• If sin (α+β)=1, then the value of sin ((α+β)/2) is:2025
• (1- tan^2 30^°)/(1+ tan^2 30^°) is equal to2025
• If x((2 tan 30^°)/(1+ tan^2 30^°))=y((2 tan 30^°)/(1- tan^2 30^°)), then x: y=2025
• If x= cos 30^°- sin 30^° and y= tan 60^°- cot 60^°, then2025
• The value of (2 tan 60^°)/(1- tan^2 60^°) is same as the value of2025
• If sin 30^° tan 45^°=(sec 60^°)/k, then the value of k is:2025
• (cos θ)/(√(1- cos^2 θ)) is equal to:2025
• A ladder 14 m long leans against a wall. If the foot of the ladder is 7 m from the wall, then the angle of elevation of the top…2025
• sec A=2 cos A is true for A=2025
• In a right triangle ABC, right-angled at A, if sin B = 1/4, then the value of sec B is2025
• Assertion: For an acute angle θ, value of cosec θ cannot be 1/(√2). Reason (R): cosec θ ≥ 1 for 0^° ≤ θ ≤ 90^°2025
• Assertion: For an acute angle θ, sin θ=3/5 ⇒ cos θ=-4/5. Reason (R): For any value of θ, (0^° ≤ θ ≤ 90^°) sin^2 θ+ cos^2 θ=1.2025
• Assertion: For an acute angle θ, sec θ=3 ⇒ tan θ=2 √2. Reason (R): sec^2 θ=1- tan^2 θ for all values of θ.2025
• If 4 k= tan^2 60^°-2 cosec^2 30^°-2 tan^2 30^°, then find the value of k.2025
• If x cos 60^°+y cos 0^°+ sin 30^°- cot 45^°=5, then find the value of x+2 y. OR Evaluate: (tan^2 60^°)/(sin^2 60^°+ cos^2 30^°)2025
• If tan A+ cot A=6, then find the value of tan^2 A+ cot^2 A-4.2025
• If a sec θ+b tan θ=m and b sec θ+a tan θ=n, prove that a^2+n^2=b^2+m^2 OR Use the identity: sin^2 A+ cos^2 A=1 to prove that…2025
• If tan A=√3; where A is an acute angle, then find the value of (sin^2 A)/(1+ cos^2 A).2025
• It is given that sin (A-B)= sin A cos B- cos A sin B. Use it to find the value of sin 15^°. OR If sin A=y, then express cos A and…2025
• Find the value of x for which ( sin A+cosec A)^2+( cos A+ sec A)^2=x+ tan^2 A+ cot^2 A OR Evaluate the following: (3 sin 30^°-4…2025
• Prove that: √(sec^2 θ+cosec^2 θ)= tan θ+ cot θ OR If cosec θ=x+1/(4 x), prove that cosec θ+ cot θ=2 x or 1/(2 x).2025
• If tan θ+ sin θ=m and tan θ- sin θ=n, then prove that m^2-n^2=4 √mn. OR Prove that: (cot A-1)/(2- sec^2 A)=(cot A)/(1+ tan A)2025
• Prove that: (1+1/(tan^2 θ))(1+1/(cot^2 θ))=1/(sin^2 θ- sin^4 θ) OR Prove that: √((cosec θ-1)/(cosec θ+1))+√((cosec θ+1)/(cosec…2025
• Prove that: (tan θ)/(1- cot θ)+(cot θ)/(1- tan θ)=1+ sec θ cosec θ OR Prove that: (sin A+ cos A)/(sin A- cos A)+(sin A- cos…2025
• Prove that: √((sec A-1)/(sec A+1))+√((sec A+1)/(sec A-1))=2 cosec A OR Prove that: (1/(cos A)- cos A)(1/(sin A)- sin A)=1/(tan A+…2025
• Prove that (cos A+ sin A-1)/(cos A- sin A+1)=cosec A- cot A OR If cot θ+ cos θ=p and cot θ- cos θ=q, prove that p^2-q^2=4 √(p q)2025
• Prove that: (cos θ-2 cos^3 θ)/(sin θ-2 sin^3 θ)+ cot θ=0. OR Given that sin θ+ cos θ=x, prove that sin^4 θ+ cos^4…2025
• Prove the following trigonometric identity: (1+cosec A)/(cosec A)=(cos^2 A)/(1- sin A) OR Let 2 A+B and A+2 B be acute angles…2025
• The distance between the points (a cos θ,-a sin θ) and (a sin θ, a cos θ) is2024
• If x/3=2 sin A, y/3=2 cos A, then the value of x^2+y^2 is:2024
• If 4 sec θ-5=0, then the value of cot θ is:2024
• If 5 tan θ-12=0, then the value of sin θ is:2024
• If sin A=2/3, then value of cot A is:2024
• If x=a cos θ and y=b sin θ, then the value of b^2 x^2+a^2 y^2 is:2024
• If sin θ= cos θ,(0^°<θ<90^°), then value of ( sec θ · sin θ) is:2024
• If sec θ- tan θ=m, then the value of sec θ+ tan θ is:2024
• If cos θ=(√3)/2 and sin φ=1/2, then tan (θ+φ) is:2024
• For θ=30^°, the value of (2 sin θ cos θ) is:2024
• If sin θ=1, then the value of 1/2 sin ((θ)/2) is:2024
• If cos (α+β)=0, then value of cos ((α+β)/2) is equal to:2024
• If sin α=(√3)/2, cos β=(√3)/2, then tan α · tan β is:2024
• The value of θ for which 2 sin^2 θ=1/2; 0^° ≤ θ ≤ 90^° is:2024
• Assertion: If sin A=1/3(0^°<A<90^°), then the value of cos A is (2 √2)/3 Reason (R): For every angle θ, sin^2 θ+ cos^2 θ=1.2024
• Evaluate: (sec^2 45^°- tan^2 45^°)/(sin^2 45^°)2024
• Evaluate: (5 tan 60^°)/(( sin^2 60^°+ cos^2 60^°) tan 30^°)2024
• Evaluate: (2 tan 30^° · sec 60^° · tan 45^°)/(1- sin^2 60^°)2024
• Evaluate: 2 √2 cos 45^° sin 30^°+2 √3 cos 30^° OR If A=60^° and B=30^°, verify that: sin (A+B)= sin A cos B+ cos A sin B2024
• Evaluate: (5 cos^2 60^°+4 sec^2 30^°- tan^2 45^°)/(sin^2 30^°+ sin^2 60^°) OR If sin (A-B)=1/2, cos ( A+B)=1/2; 0<A+B ≤ 90^°,…2024
• Evaluate: 2 sin^2 30^° sec 60^°+ tan^2 60^°. OR If 2 sin ( A+B)=√3 and cos (A-B)=1, then find the measures of angles A and B.0 ≤…2024
• Evaluate: (cos 45^°+ sin 60^°)/(sec 30^°+cosec 30^°).2024
• Evaluate: (2 tan 30^° · sec 60^° · tan 45^°)/(1- sin^2 60^°) This section comprises Short Answer (SA) type questions of 3 marks…2024
• Prove that (sin θ- cos θ+1)/(sin θ+ cos θ-1)=1/(sec θ- tan θ)2024
• Prove that (cosec^2 θ- sec^2 θ)/(cosec^2 θ+ sec^2 θ)=3/4, if tan θ=1/(√7)2024
• Prove that: (tan θ- cot θ)/(sin θ cos θ)= sec^2 θ-cosec^2 θ2024
• Prove that (sin A+ cos A)/(sin A- cos A)+(sin A- cos A)/(sin A+ cos A)=2/(2 sin^2 A-1)2024
• Prove that: (tan θ)/(1- cot θ)+(cot θ)/(1- tan θ)=1+ sec θ cosec θ2024
• If sin θ+ cos θ=p and sec θ+cosec θ=q, then prove that q(p^2-1)=2 p.2024
• Prove that (1+ sec θ- tan θ)/(1+ sec θ+ tan θ)=(1- sin θ)/(cos θ).2024
• Prove that: (tan A)/(1- cot A)+(cot A)/(1- tan A)=1+ sec A cosec A2024
• Prove that (sin θ-2 sin^3 θ)/(2 cos^3 θ- cos θ)= tan θ.2024
• Prove that: (sin θ)/(1+ cos θ)+(1+ cos θ)/(sin θ)=2 cosec θ2024
• Prove that sin^6 θ+ cos^6 θ=1-3 sin^2 θ cos^2 θ.2024
• Prove that: (cosec θ- sin θ)( sec θ- cos θ)( tan θ+ cot θ)=1 This section consists of 4 questions of 5 marks each.2024
• Prove that √(sec^2 θ+cosec^2 θ)= tan θ+ cot θ. This section comprises Long Answer (LA) type questions of 5 marks each. 4 × 5=202024
• ((1- tan^2 30^°)/(1+ tan^2 30^°)) is equal to:2023
• Which of the following is true for all values of θ(0^° ≤ θ ≤ 90^°)?2023
• If tan θ=x/y, then cos θ is equal to2023
• If 2 tan A=3, then the value of (4 sin A+3 cos A)/(4 sin A-3 cos A) is2023
• If tan θ=5/12, then the value of (sin θ+ cos θ)/(sin θ- cos θ) is:2023
• (cos^2 θ)/(sin^2 θ)-1/(sin^2 θ), in simplified form, is:2023
• ( sec^2 θ-1)(cosec^2 θ-1) is equal to:2023
• If sec θ- tan θ=1/3, then the value of ( sec θ+ tan θ) is:2023
• [3/4 tan^2 30^°- sec^2 45^°+ sin^2 60^°] is equal to2023
• sec θ when expressed in terms of cot θ, is equal to:2023
• ((2 tan 30^°)/(1+ tan^2 30^°)) is equal to:2023
• The hour-hand of a clock is 6 cm long. The angle swept by it between 7:20 a.m. and 7:55 a.m. is:2023
• If θ is an acute angle of a right angled triangle, then which of the following equation is not true?2023
• [5/8 sec^2 60^°- tan^2 60^°+ cos^2 45^°] is equal to2023
• ( cos^4 A- sin^4 A) on simplification, gives2023
• Statement A (Assertion): For 0<θ ≤ 90^°, cosec θ- cot θ and cosec θ+ cot θ are reciprocal of each other. Statement R (Reason):…2023
• If sin θ+ sin^2 θ=1, then prove that cos^2 θ+ cos^4 θ=1. OR If tan θ=1/(√7), then show that (cosec^2 θ- sec^2 θ)/(cosec^2 θ+…2023
• Evaluate: 5/(cot^2 30^°)+1/(sin^2 60^°)- cot^2 45^°+2 sin^2 90^° OR If θ is an acute angle and sin θ= cos θ, find the value of…2023
• If 4 cot^2 45^°- sec^2 60^°+ sin^2 60^°+p=3/4, then find the value of p. OR If cos A+ cos^2 A=1, then find the value of sin^2 A+…2023
• Evaluate 2 sec^2 θ+3 cosec^2 θ-2 sin θ cos θ if θ=45^°. OR If sin θ- cos θ=0, then find the value of sin^4 θ+ cos^4 θ.2023
• If sin θ+ cos θ=√3, then find the value of sin θ · cos θ. OR If sin α=1/(√2) and cot β=√3, then find the value of cosec α+cosec β.2023
• If a cos θ+b sin θ=m and a sin θ-b cos θ=n, then prove that a^2+b^2=m^2+n^2. Prove that: √((sec A-1)/(sec A+1))+√((sec A+1)/(sec…2023
• If a cos θ+b sin θ=m and a sin θ-b cos θ=n, then prove that a^2+b^2=m^2+n^2. OR Prove that: √((sec A-1)/(sec A+1))+√((sec…2023
• Evaluate (5 cos^2 60^°+4 sec^2 30^°- tan^2 45^°)/(sin^2 30^°+ cos^2 30^°) OR If A and B are acute angles such that sin (A-B)=0…2023
• Prove that: (sin θ)/(1+ cos θ)+(1+ cos θ)/(sin θ)=2 cosec θ2023
• Prove that ( sin θ+ cos θ)( tan θ+ cot θ)= sec θ+cosec θ.2023
• Prove that: (cos^2 θ)/(1- tan θ)+(sin^3 θ)/(sin θ- cos θ)=1+ sin θ cos θ2023
• If sin θ+ cos θ=p and sec θ+cosec θ=q, then prove that q(p^2-1)=2 p.2023
• Prove that: 2( sin^6 θ+ cos^6 θ)-3( sin^4 θ+ cos^4 θ)+1=0.2023
• Prove that: (1/(cos θ)- cos θ)(1/(sin θ)- sin θ)=1/(tan θ+ cot θ).2023
• Prove that: (tan A)/(1+ sec A)-(tan A)/(1- sec A)=2 cosec A2023
• Prove that (sin A-2 sin^3 A)/(2 cos^3 A- cos A)= tan A OR Prove that sec A(1- sin A)( sec A+ tan A)=1.2023
• Prove that: (tan θ+ sec θ-1)/(tan θ- sec θ+1)=(1+ sin θ)/(cos θ)2023
• Prove that: (tan θ)/(1- cot θ)+(cot θ)/(1- tan θ)=1+ sec θ cosec θ2023
• Prove that (1+ sec A)/(sec A)=(sin^2 A)/(1- cos A).2023
• Prove that (cosec A- sin A)( sec A- cos A)=1/(cot A+ tan A).2023
• The sum of two numbers is 34. If 3 is subtracted from one number and 2 is added to another, the product of these two numbers…2022

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