CPM Homework Help : PCT Problem 7-97

Simplify: $(1+2\sin(θ))^2+(2\cos(θ))^2$

Step 1:

Expand each of the squared terms.

$1+4\sinθ+4\sin^2θ+4\cos^2θ$

Step 2:

Factor $4$ out of the squared terms.

$1+4\sinθ+4(\sin^2θ+\cos^2θ)$

Step 3:

Use the Fundamental Pythagorean Identity to simplify.

$1+4\sinθ+4$

Step 4:

Simplify.