# Homework Help: Trigonometric identities.

1. Aug 12, 2011

### hibernator

1. The problem statement, all variables and given/known data

prove that sin^4theta + cos^4 theta =1/4 (3+cos4theta).hence,find the greatest and least value of sin^4theta + cos^4 theta.

please give hints to start . no idea at all...i start from the RHS and get 2cos^4 theta - 2 cos^2 theta +1 , then how sin^4theta + cos^4 theta

2. Relevant equations

3. The attempt at a solution

2. Aug 12, 2011

### eumyang

So you started at the RHS and got to this:
2cos4 θ - 2cos2 θ + 1.
You're really close, then. Split the 2cos4 θ and rearrange the terms like so:
cos4 θ + 1 - 2cos2 θ + cos4 θ
Factor the part in bold.

Last edited: Aug 12, 2011
3. Aug 12, 2011

### hibernator

Amazing idea that i never thought before !! TQ so much eumyang..