Question

Pls prove that cos^4A-cos^2A=sin^4A-sin^2A​

Answer 1

Step-by-step explanation:

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

= sin ^4A-sin ^2A = R.H.S

Answer 2

Question : cos⁴A - cos²A = sin⁴ - sin²A

SOLUTION :

From LHS,

= cos⁴A - cos²A

Take out cos²A as common factor.

= cos²A( cos²A - 1)

= -cos²A(1 - cos²A)

We know that,

1 - cos²A = sin²A

= cos²A.sin²A

we know that,

cos²A = 1 - sin²A

= 1 - sin²A.sin²A

= sin²A - sin⁴A

= sin⁴A - sin²A

Hence, Proved !!