Question

Cosec/cosec-1+cosec/cosec+1=2sec`2

Answer 1

$l.h.s = \frac{ \csc( \alpha ) }{ \csc( \alpha ) - 1 } + \frac{ \csc( \alpha ) }{ \csc( \alpha ) + 1} \\ = \frac{ \csc( \alpha )( \csc( \alpha ) + 1) + \csc( \alpha )( \csc( \alpha ) - 1) }{( \csc( \alpha ) - 1)( \csc( \alpha ) + 1) } \\ = \frac{ {csc}^{2} \alpha + csc \alpha + {csc}^{2} \alpha - csc \alpha }{ {csc }^{2} \alpha - 1 } \\ = \frac{2 {csc}^{2} \alpha }{ {csc}^{2} \alpha - 1 } \\ = \frac{2 + 2 {cot}^{2} \alpha }{ {cot}^{2} \alpha } \\ = 2 {tan}^{2} \alpha + 2 \\ = 2( {tan}^{2} \alpha + 1) \\ = 2 {sec}^{2} \alpha = r.h.s$
proved

Answer 2

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In this attachment your answer :

How To solve this type of questions

1) You should always change into sin and cos theta

2) You should try more and more questions which increase your confidence because confidence is very important in trigonometry.