✓ Board-verified
Mathematics · 2026 · 2 marks
CBSE 2026 · Region 2 · Set 2 · Q22
Evaluate : \[\frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-\tan ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}} \]Prove that : \[1+\frac{\cot ^{2} \alpha}{1+\operatorname{cosec} \alpha}=\operatorname{cosec} \alpha \]
Evaluate : \[\frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-\tan ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}} \]
Prove that : \[1+\frac{\cot ^{2} \alpha}{1+\operatorname{cosec} \alpha}=\operatorname{cosec} \alpha \]
Marking-scheme solution
\(\displaystyle \frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-\tan ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}}\)
\(\displaystyle =\frac{5\left(\dfrac{1}{2}\right)^{2}+4\left(\dfrac{2}{\sqrt{3}}\right)^{2}-(1)^{2}}{1}\)
\(\displaystyle =\frac{67}{12}\)
LHS \(\displaystyle =1+\frac{\cot ^{2} \alpha}{1+\operatorname{cosec} \alpha}\)
\(\displaystyle =1+\frac{(\operatorname{cosec} \alpha+1)(\operatorname{cosec} \alpha-1)}{(1+\operatorname{cosec} \alpha)}\)
\(\displaystyle =1+\operatorname{cosec} \alpha-1\)
\(\displaystyle =\operatorname{cosec} \alpha=\) RHS
More from Introduction to Trigonometry
- 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+…2026 · asked 3×
- 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 · asked 3×
- If sin θ= cos θ,(0^°<θ<90^°), then value of ( sec θ · sin θ) is:2024 · asked 3×
- Given that sin 2 α=(√3)/2, the value of sin 3 α is:2026 · asked 3×
- Which of the following statements is true?2025 · asked 3×
- 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 · asked 3×
- If 2 tan A=3, then the value of (4 sin A+3 cos A)/(4 sin A-3 cos A) is2023 · asked 3×
- 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+…2024 · asked 3×
CBSE Class 10 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.