Question

Prove that secA (1 - sinA) (secA + tanA) = 1​

Answer 1

Proof

Let us start with LHS

= (secA-sinA×secA)(secA+tanA)

=(secA-tanA) (secA+tanA) { secA=1/cosA and sinA/cosA=tanA}

= (sec²A-tan²A) { (a+b)(a-b)=a²-b²}

=sec²A-tan²A

=1

= RHS {using identity}

Hence proved.

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Answer 2

Answer:

Let us start with LHS

= (secA-sinA×secA)(secA+tanA)

=(secA-tanA) (secA+tanA) { secA=1/cosA and sinA/cosA=tanA}

= (sec²A-tan²A) { (a+b)(a-b)=a²-b²}

=sec²A-tan²A

=1

= RHS {using identity}

Hence proved.

" Hope it helps :) "