Question

Simplify secA(1 - sinA) (secA + tanA)

Answer 1

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.