4(sin(^4)x + cos(^4)x)=cos4x + 3

How would I solve this inequality.

I have tried solving it from LHS, by making all the terms = sinx

I have got 4(1-2cos(^2)x +2cos(^4)x)

I have now tried using algebraic division to find out what x equals. But I think this is wrong

Any suggestions and help will be appreciated

This isn't an inequality. It's an identity. You're not meant to be finding x. You're meant to show it holds for all x.

Can you see how to? Just use double angle identities a few times.

i would start on the left...

sin⁴x can be written as sin²xsin²x

and sin²x can be written as 0.5 { 1 - Cos2x }

Where does the 0.5 come from?