Question

How do you simplify `(sin theta + cos theta) ^2`?

Answer 1

`(sin(theta) +cos(theta))^2 = sin(2theta) + 1`

Explanation:

`(sin(theta) +cos(theta))^2 = sin^2(theta) + 2sin(theta)cos(theta) + cos^2(theta)`

We know that `sin^2(theta) + cos^2(theta) = 1` so

`(sin(theta) +cos(theta))^2 = 2sin(theta)cos(theta) + 1`

However, `2sin(theta)cos(theta) = sin(2theta)` so we can say

`(sin(theta) +cos(theta))^2 = sin(2theta) + 1`