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