Question

Prove: sin theta - sin theta * cos^2 theta = sin^3 theta.

help really don't get this!!! please!!

Answer 1

anyone......

Answer 2

@ganeshie8 @mathmale

Answer 3

Sin theta(1-cos^theta)
=sin theta*sin^2theta
=?

Answer 4

start with left hand side :
\[\sin\theta - \sin\theta *\cos^2\theta\]

Answer 5

factor out \(\sin\theta\) from both the terms :

\[\sin\theta - \sin\theta *\cos^2\theta = \sin\theta[1- \cos^2\theta ]\]

Answer 6

okay got it

Answer 7

good, use the identity \(\sin^2\theta + \cos^2\theta = 1\) and write \(1-\cos^2\theta\) as \(\sin^2\theta\)

Answer 8

how do I do that??

Answer 9

\[\sin\theta - \sin\theta *\cos^2\theta = \sin\theta[1- \cos^2\theta ] = \sin\theta[\sin^2\theta] = \sin^3\theta\]