How do you prove $(sinx/(cscx-1))+(sinx/(csc+1))=2tan^2x$ ?

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Answer 1 · 2018-03-04T07:12:22

Given,

$((sin x)/(cscx-1)) +((sinx)/(csc x+1))$

$=(sinx(cscx+1) + sinx(cscx-1))/((cscx+1)(cscx-1))$

$=(sinx(csc x+1 + cscx-1))/(csc^2 x -1)$

$=(sinx 2 cscx)/(cot^2 x)$ (as, $csc^2 x - cot^2 x=1$ )

$=((2 sinx)/(sinx))/cot^2 x$

$=2/cot^2 x$

$=2 tan^2 x$

How do you prove (sinx/(cscx-1))+(sinx/(csc+1))=2tan^2x(sinx/(cscx-1))+(sinx/(csc+1))=2tan^2x?