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Question: \(\sin^{2}(ix) + {\cos h}^{2}x\) is equal to....

sin⁡2(ix)+cos⁡h2x\sin^{2}(ix) + {\cos h}^{2}x is equal to.

A

1

B

– 1

C

2cosh⁡2x2\cosh^{2}x

D

cos⁡h2x{\cos h}2x

Answer

1

Explanation

Solution

We know that sin⁡ix=isin⁡hx\sin ix = i{\sin h}x

sin⁡2(ix)=(isinh⁡x)2=−sin⁡h2x\sin^{2}(ix) = (i\sinh x)^{2} = - {\sin h}^{2}x

∴sin⁡2(ix)+cos⁡h2x=cos⁡h2x−sin⁡h2x=1\sin^{2}(ix) + {\cos h}^{2}x = {\cos h}^{2}x - {\sin h}^{2}x = 1.