Question

prove that..... secA (1-sinA)(secA+tanA)=1

Answer 1

I hope you will be able to understand

Answer 2

Proof :

$Now, secA (1 - sinA)(secA + tanA)\\ \\ = secA (1-sinA)(\frac{1}{cosA}+\frac{sinA}{cosA})\\ \\ =secA (1-sinA)(\frac{1+sinA}{cosA})\\ \\ =\frac{secA}{cosA}(1-sinA)(1+sinA)\\ \\ =sec^{2}A (1-sin^{2}A)\\ \\ =(sec^{2}A)(cos^{2}A)\\ \\ =(secA\:cosA)^{2}\\ \\ =1^{2}\\ \\ =1$

Hence, proved.

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