Question

If $\cos ec\theta =cothx$, then the value of $\tan \theta$ is

• A. $\cos hx$
• B. $\sin hx$
• C. $\tan hx$
• D. $\cos echx$

Answer 1

The correct option is B

$\sin hx$

Explanation for the correct option:

Step 1. Simplify the given data:

Here $\cos ec\theta =cothx$

We will take square of both side of the given equation:

$\cos e{c}^2\theta =co{t}^{2}hx$

$\Rightarrow$$1+co{t}^2\theta =cot{h}^{2}x$ $\left[\mathbf{\because }\mathit{c}\mathit{o}\mathit{s}\mathit{e}{\mathit{c}}^{\mathbf{2}}\mathit{\theta }\mathbf{}\mathbf{-}\mathbf{}\mathit{c}\mathit{o}{\mathit{t}}^{\mathbf{2}}\mathit{\theta }\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\right]$

$\Rightarrow$ $co{t}^2\theta =cot{h}^{2}x–1$

$\Rightarrow$ $co{t}^2\theta =\cos ec{h}^{2}x$ $\left[\mathbf{\because }\mathit{c}\mathit{o}\mathit{s}\mathit{e}\mathit{c}\mathbf{}{\mathit{h}}^{\mathbf{2}}\mathit{\theta }\mathbf{}\mathbf{+}\mathbf{}\mathbf{1}\mathbf{}\mathbf{=}\mathbf{}\mathit{c}\mathit{o}\mathit{t}\mathbf{}{\mathit{h}}^{\mathbf{2}}\mathit{\theta }\right]$

Step 2. Find the value of $\tan \theta$

We got, $cot\theta =\cos echx$

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

Hence, option (B) is correct answer.