Question

Complete the identity (sin x +cos x) ^2

Please please help

Answer 1

Explanation:

Using perfect square trinomial rules,

`(a + b) {}^(2) = {a}^(2) + 2ab + {b}^(2)`

Here, a is sin x

b is cos x

So

`( \sin(x) + \cos(x) ) {}^(2) = \sin {}^(2) (x) + 2 \sin(x) \cos(x) + \cos {}^(2) (x)`

We know

`\sin {}^(2) (x) + \cos {}^(2) (x) = 1`

So we know have

`1 + 2 \sin(x) \cos(x)`

`\sin(2x) = 2 \sin(x) \cos(x)`

So our final answer is

`1 + \sin(2x)`