Question

Prove that cos^4a- sin^4a +1 = 2cos^2a

Answer 1

Answer:

cos^4a- sin^4a +1 = 2cos^2a

LHS:

(cos²a)² - (sin²a)² +1

= (cos²a + sin²a) (cos²a-sin²a) + 1

= 1(cos²a-sin²a) + 1

= cos²a - (1- cos²a)+ 1

= cos²a - 1 + cos²a+ 1

= 2 cos²a  = RHS

Hope this helps. Happy learning!!!