Jitender Gupta and Divya Malik Solutions for Exercise 2: ARCHIVES (Last 8 Years)

Prove that $(1+\cot \theta -\mathrm{cosec} \theta )(1+\tan \theta +\sec \theta )=2$

Evaluate without using trigonometric table

${\sin }^2{28}^0+{\sin }^2{62}^0+{\tan }^2{38}^0-{\cot }^2{52}^0+\frac{1}{4}{\sec }^2{30}^0$

 Prove that: $\frac{\sin \theta -2{\sin }^3\theta }{2{\cos }^3\theta -\cos \theta }=\tan \theta$

Without using trigonometric tables, evaluate: ${\mathrm{cosec}}^2 57°-{\tan }^2 33°+\cos 45° \mathrm{cosec} 45°-\sqrt{2 }\cos 45°-{\tan }^2 60°$

Prove that $\frac{\cos A}{1+\sin A}+\tan A=\mathrm{secA}$

Prove that: $\frac{\mathrm{cosA}}{1-\mathrm{tanA}}+\frac{\sin {\displaystyle \mathrm{A}}}{1-\mathrm{cotA}}=\mathrm{cosA}+\mathrm{sinA}$

Prove that: $\frac{\sin \theta }{1-cot\theta }+\frac{\cos {\displaystyle \theta }}{1-\tan \theta }=\cos \theta +\sin \theta$

Without using trigonometric tables, evaluate,

${\sin }^2 34 ° + {\sin }^2 56 ° + 2 \tan 18 ° \tan 72 ° -{\cos }^2 30° .$