Question

1.) Simplify the expression.

Answer 1

Answer:

$sin ( u +\frac{\pi}{2} ) = cos (u)$

Step-by-step explanation:

Let us use the identity

sin(A+B)=  cos(A) sin(B)+cos (B) sin(A) to simplify the given expression

Then

$sin(u + \frac{\pi}{2})= \cos \left(u\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(u\right)$--------------------(1)

Here

$cos (\frac{\pi}{2}) = 0$---------------------(2)

$sin(\frac{\pi}{2})= 1$---------------------(3)

Substituting the values  in (1)

$sin(u + \frac{\pi}{2})= \cos \left(u\right)(1)+(0)\sin \left(u\right)$

$sin(u + \frac{\pi}{2})= \cos \left(u\right) + 0$

$sin(u + \frac{\pi}{2})= \cos \left(u\right)$