This is similar to a question i seen below but how do i write cos^2 4-sin^2 4 as a single trigonometric function?

Question

And 1-2sin^2 3

Answer 1

Have you come across this identity and its variations?

cos 2A = cos^2 A - sin^2 A
= 1 - 2sin^2 A
= 2cos^2 A - 1

so ....
cos^2 4-sin^2 4
= 1 - sin^2 4 - sin^2 4
= 1 - 2sin^2 4
= cos 8

1 - 2sin^2 3
= cos 6