Question

Prove :
cos A/(cosec A+1) + cos A/(cosec A-1) = 2 tan A.

Answer 1

$\frac{cosA}{cosecA+1} + \frac{cosA}{cosecA-1} \\ \\= \frac{cosA}{ \frac{1}{sinA} +1} + \frac{cosA}{ \frac{1}{sinA } -1}\\ \\ =\frac{cosA}{ \frac{1+sinA}{sinA} } + \frac{cosA}{ \frac{1-sinA}{sinA }}\\ \\ =\frac{sinA.cosA}{1+sinA} + \frac{sinA.cosA}{1-sinA}\\ \\=sinA.cosA[\frac{1}{1+sinA} + \frac{1}{1-sinA}]\\ \\=sinA.cosA[\frac{1-sinA+1+sinA}{1-sin^2A}]\\ \\ =\frac{2sinA.cosA}{cos^2A}\\ \\=\frac{2sinA}{cosA}\\ \\=2tanA$

Answer 2

Answer:

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Step-by-step explanation: