Question

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

Answer 1

Taking LHS,

= cos⁴A - cos²A

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 !!