Simplify sin^4x+sin^2x(cos^2x)

Question

Please show all work so it is easy to understand.

Answer 1

Simplify sin⁴x + sin²x * cos²x

Use the Pythagorean Identity: sin²x + cos²x = 1, with the variants:

cos²x = 1 - sin²x

sin²x = 1 - cos²x

Replace cos²x in the original expresssion:

sin⁴x + sin²x *( 1 - sin²x )

sin⁴x - sin⁴x + sin²x

sin²x

Answer 2

sin^4x+sin^2x(cos^2x)

factor out sin^2x

sin^2x(sin^2x+cos^2x)

sin^2x*1

sin^2x is the answer

sin^2x is the answer because sin^2x+cos^2x=1