Question

tan^2theta-sin^2theta= sin^4theta×sec^2theta.​ prove the following.

Answer 1

Answer:

I'll type A instead of theta.

tan²A - sin²A = sin⁴A x sec²A

=> sin²A/cos²A - sin²A = sin⁴A/cos²A

Multiply both sides by cos²A

=> sin²A - sin²Acos²A = sin⁴A

=> sin²A( 1 - cos²A) = sin⁴A

As 1 - cos²A = sin²A,

=> sin²A(sin²A) = sin⁴A

=> sin⁴A = sin⁴A

Therefore, L.H.S = R.H.S

Hence proved.