Question

CosA/cosecA+1+cosA/cosecA-1=2tanA

Answer 1

hope this will help you

Answer 2

$LHS = \frac{cosA }{Cosec A + 1 } + \frac{cosA }{Cosec A - 1 } \\= cosA \Big( \frac{1 }{Cosec A + 1 } + \frac{1 }{Cosec A - 1 }\Big) \\= cosA\Big( \frac{cosecA - 1 + Cosec A + 1 }{(cosecA+1)(cosecA-1)}\Big) \\= cosA\Big( \frac{2cosecA}{cosec^{2} A - 1^{2} } \Big) \\= \frac{2cosAcosecA}{cot^{2} A }$

$\blue { By \: Trigonometric \:Identity )}$

$\boxed { \pink {Cosec^{2} A - 1 = cot^{2} A }}$

$= \frac{2cosA \times \frac{1}{sinA}}{cot^{2} A }\\= \frac{2cotA}{cot^{2}A} \\= \frac{2}{cotA} \\= 2 tan A \\= RHS$

Therefore.,

$\red {\frac{cosA }{Cosec A + 1 } + \frac{cosA }{Cosec A - 1 }} \green{= 2tan A }$

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