Question

${\sin }^{2}ix+\cos h^{2}x=$

• A. $1$
• B. $-1$
• C. $2\cos h^{2}x$
• D. $\cos hx$

Answer 1

The correct option is A

$1$

Explanation for the correct answer:

Simplifying the given expression:

We know that, $\sin ix=i\sin hx$

Also,

$$\begin{gathered} {\sin }^2\left(ix\right)={(i\sin hx)}^2 \\ =–\sin h^{2}x[\because i^2=-1] \end{gathered}$$

Now,

$$\begin{gathered} \Rightarrow {\sin }^{2}ix+\cos h^{2}x \\ \Rightarrow \cos h^{2}x–\sin h^{2}x[\because \cos h^{2}x–\sin h^{2}x=1] \\ \Rightarrow 1 \end{gathered}$$

Therefore, the correct answer is option (A).