Question

cosec²θ / cosec θ -1 - cosec²θ / cosecθ + 1 = 2 sec²θ
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Answer 1

Answer:

Hey there

$= \frac{ { \csc( \alpha ) }^{2} }{ \csc( \alpha ) - 1 } - \frac{ { \csc( \alpha ) }^{2} }{ \csc( \alpha ) + 1} \\ = \frac{ { \csc( \alpha ) }^{2}( \csc( \alpha ) + 1) - { \csc( \alpha ) }^{2}( \csc( \alpha ) - 1) }{( \csc( \alpha ) + 1)( \csc( \alpha ) - 1) } \\ = \frac{ { \csc( \alpha ) }^{2} ( \csc( \alpha ) + 1 + \csc( \alpha ) - 1) }{ { \csc( \alpha ) }^{2} - 1} \\ = \frac{ { \csc( \alpha ) }^{2} \times 2 \csc( \alpha ) }{ { \cot( \alpha ) }^{2} } \\ = \frac{2 { \sin( \alpha ) }^{2} }{ { \sin( \alpha ) }^{3} { \cos( \alpha ) }^{2} } \\ = 2 { \sec( \alpha ) }^{2} \csc( \alpha )$

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Answer 2

Answer:

See the attachment.

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