How can you simplify sin4a+cos4a?

1 Answer
Jul 17, 2017

sin4a+cos4a=12sin2acos2a=112sin2(2a).

Explanation:

Note that

(sin2a+cos2a)2=sin4a+2sin2acos2a+cos4a

We see that sin2x+cos2x=1, so that

1=sin4a+2sin2acos2a+cos4a

Therefore,

sin4a+cos4a=12sin2acos2a

Hopefully this helps!