Question

if alpha+beta=90,sin alpha/cosec beta

Answer 1

alpha = 90 - beta

=> sin alpha/ cosec beta

(1/cosec beta = sin beta)

=> sin alpha x sin beta

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Answer 2

given that

$\alpha + \beta = 90$

$\alpha = 90 - \beta$

given

$\frac{ \sin( \alpha ) }{ \csc( \beta ) }$

put the value of alpha

$\frac{ \sin(90 - \ \beta ) }{ \csc( \beta ) }$

formula

$\sin(90 - \ \beta ) = \cos( \ \beta )$

$\frac{ \cos( \ \beta ) }{ \csc( \beta ) }$

$\cos( \beta ) \sin( \beta )$

final answer