Question

Question #c1e7d

Answer 1

Please see the explanation

Explanation:

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

I will only make changes to the left side.

Expand the square:

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

Move the swap the second and third terms:

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

Use the identity `1 = sin^2(theta) + cos^2(theta)`:

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

Verified.