Question

prove that (1+tan A) ² + (1-tan A) ² = 2sec²A​

Answer 1

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Let's solve this by taking R.H.S. and L.H.S.

Take R.H.S. 2sec²A

Take left hand side of the equation (1+tanA)²+(1-tanA)²=2sec²A

L.H.S.= (1+tanA)²+(1-tanA)²= 1+tan²A+ 2tanA + 1 tan²A+2 tanA

=2+2 tan²A

=2+1 tan²A

=2 sec²A

Hence L.H.S. = R.H.S.

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