### Home > PC > Chapter 7 > Lesson 7.3.1 > Problem7-97

7-97.

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

Expand each of the squared terms.

$1+4\sinθ+4\sin^2θ+4\cos^2θ$

Factor $4$ out of the squared terms.

$1+4\sinθ+4(\sin^2θ+\cos^2θ)$

Use the Fundamental Pythagorean Identity to simplify.

$1+4\sinθ+4$

Simplify.