How to Find Maximum and Minimum Values of Sin^4theta + Cos^4theta

[hibernator]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[eumyang]

Homework Statement

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

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.

 

[hibernator]

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