Introduction to Trigonometry

CBSE Class 10 Mathematics · every board question from this chapter, 2025–2025 · 18 of them repeated across years

• If tan 3 θ=√3, then (θ)/2 equals:2025asked 2×
• 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:2025asked 2×
• If sin 4 θ=(√3)/2, then (θ)/3 equals:2025
• The value of tan^2 θ-(1/( cos θ) × sec θ) is:2025asked 2×
• tan 2 A=3 tan A is true, when the measure of ∠ A is:2025
• ( cot θ+ tan θ) equals:2025asked 2×
• Which of the following statements is true?2025asked 3×
• Which of the following is a trigonometric identity?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:2025asked 3×
• 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 is2025asked 3×
• 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
• If 4 k= tan^2 60^°-2 cosec^2 30^°-2 tan^2 30^°, then find the value of k.2025asked 2×
• 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^°)2025asked 3×
• 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…2025asked 3×
• If tan A=√3; where A is an acute angle, then find the value of ( sin^2 A)/(1+ cos^2 A).2025asked 3×
• 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…2025asked 3×
• 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…2025asked 3×
• 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…2025asked 3×
• 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…2025asked 3×
• 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 q2025asked 3×
• 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…2025asked 3×
• 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…2025asked 3×

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