Question

cos^4(theta) - sin^4(theta)​

Answer 1

Answer:

Step-by-step explanation:

Cos^4A - Sin^4A = ?

= (cos^2)^2 - (sin^2)^2

*By Identity - (a^2 - b^2) = (a+b) (a-b)

*Here, a = cos^2

b = sin^2

= (cos^2 A + sin^2 A) (cos^2A - sin^2 A)

*By identity, cos^2A + sin^2A = 1

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

*By identity, cos^2 A = 1 - sin^2 A

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

= 1 - 2(sin^2 A)