cos^4 a + cos^2 - sin^4 - sin^2 a=?

Question

cos^4 a + cos^2 - sin^4 - sin^2 a=?

Answer 1

cos^4 a + cos^2 - sin^4 - sin^2 a =

(cos^4 a - sin^4 a) + (cos^2 a - sin^2 a) = 

(cos^2 a + sin^2 a)(cos^2 a - sin^2 a) + cos2a =

cos2a + cos2a = 2cos2a