Question

Prove cos⁴A - cos²A = sin⁴A - sin²A.

Answer 1

Prove cos⁴A - cos²A = sin⁴A - sin²A.

Good question,

Here is your perfect answer!

= cos²A(cos²A - 1)

Since cos²A = 1 - sin²A,

= (1 - sin²A) (1-sin²A-1)

= (1 - sin²A) (-sin²A)

= - sin²A + sin⁴A

= sin⁴A - sin²A

LHS = RHS, proved.

Answer 2

cos^4 A-cos^2 A=LHS

sin^4 A-sin^2 A=RHS

as we know,

cos (90-A)=sin A

therefore,

cos^4(90-A)=sin^4 A .....equation 1

cos^2 (90-A)=sin^2 A.....equation 2

therefore combining equation 1 and 2

we get

cos^4 A - cos^2 A =sin^4 A - sin^2 A

therefore LHS = RHS

HENCE PROVED. ..