Using trig Identities, I need to solve this question

Question

sinxcos^4x+cos^6x=

Answer 1

Use the identity            sin²x + cos²x = 1

 

sinx(1 - sin²x)² + (1 - sin²x)³

 

 

Let          q = sinx

 

q(1 - q²)² + (1 - q²)³

 

 

Factor out (1 - q²)².

 

(1 - q²)²[q + (1 - q²)] =

 

(1 - q²)²[q + 1 - q²] =

 

(1 - 2q² + q⁴)(1 + q - q²) =

 

(1 - 2sin²x + sin⁴x)(1 + sinx - sin²x) =

 

(1 - sin²x)(1 - sin²x)(1 + sinx - sin²x)

 

This is what I got.  An expression using only one trig function.