Question

If $\cos hz=sec\theta$, then $\sin hz=?$

• A. $\cos ec\theta$
• B. $cot\theta$
• C. $\tan \left(\frac{\theta }{2}\right)$
• D. $\tan \theta$

Answer 1

The correct option is D

$\tan \theta$

Find the value of $\mathit{s}\mathit{i}\mathit{n}\mathbf{}\mathit{h}\mathit{z}$:

Given, $\cos hz=sec\theta$

As we know,

$\mathit{c}\mathit{o}\mathit{s}\mathbf{}{\mathit{h}}^{\mathbf{2}}\mathit{z}\mathbf{}\mathbf{–}\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathbf{}{\mathit{h}}^{\mathbf{2}}\mathit{z}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}$

$\Rightarrow$ $\sin h^{2}z=\cos h^{2}z–1$

$\Rightarrow$ $\sin h^{2}z=se{c}^2\theta –1$

$\Rightarrow$ $\sin h^{2}z={\tan }^2\theta$ $\left[\mathbf{\because }\mathit{s}\mathit{e}{\mathit{c}}^{\mathbf{2}}\mathit{\theta }\mathbf{}\mathbf{-}\mathbf{}\mathit{t}\mathit{a}{\mathit{n}}^{\mathbf{2}}\mathit{\theta }\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\right]$

$\Rightarrow$ $\mathit{s}\mathit{i}\mathit{n}\mathbf{}\mathit{h}\mathit{z}\mathbf{}\mathbf{=}\mathbf{}\mathit{t}\mathit{a}\mathit{n}\mathbf{}\mathit{\theta }$

Hence, Option ‘D’ is Correct.