R. D. Sharma Solutions for Chapter: Trigonometric Ratios, Exercise 3: EXERCISE 10.3

Evaluate the following:
 $\frac{\tan 35°}{\cot 55°}+\frac{\cot 78°}{\tan 12°}-1$

Express the following in terms of trigonometric ratios of angles lying between $0°$ and $45°$

$\sec 76°+\mathrm{cosec} 52°$

Express the following in terms of trigonometric ratios of angles lying between $0°$ and $45°$

$\cos 78°+\sec 78°$

If $\cos 2\theta =\sin 4\theta ,$ where $2\theta$ and $4\theta$ are acute angles, find the value of $\theta$.

If $\sin 3\theta =\cos \left(\theta -6°\right)$, where $3\theta$ and $\theta -6°$ are acute angles, find the value of $\theta$.

If $\sec 4A=\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{c}\left(A-20°\right)$, where $4A$ is an acute angle, find the value of $A$.

If $\sec 2A=\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{c}\left(A-42°\right)$ where $2A$ is an acute angle, find the value of $A$.

If $\tan 2\mathrm{A}=\cot (\mathrm{A}-18°)$, where $2\mathrm{A}$ is an acute angle, find the value of $\mathrm{A}$.