prove the following identity sin²x + cos4x = cos2x + sin4x trig identity

Question

prove this following identity by using a variety of formula and identities

Answer 1

The identity Sin^2x+Cos^4x = Cos^2x+Sin^4x

We are able to write the above identity

Sin^4x-Cos^4x = Sin^2x-Cos^2x

Now left handside identity

= Sin^4x-Cos^4x

= (Sin^2x-Cos^2x)(Sin^2x+Cos^2x)

We know that Sin^2x+Cos^2x = 1

= Sin^2x-Cos^2x

= Right hand side identity