Verfiy the identity sinx(cscx + sinxsec^2x)= sec^2 x?

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Answer 1 · 2017-10-31T17:47:39

see below

$sinx(cscx + sinx sec^2 x)=sec^2x$

Left Hand Side:

$=sinx(cscx + sinx sec^2 x)$

$=sin x cscx+sin^2xsec^2x$ ---> Distribute

$=sinx* 1/sinx+sin^2x*1/cos^2x$

$=cancelsinx* 1/cancelsinx+sin^2x/cos^2x$

$=1+tan^2x$

$=sec^2x$

$=$ Right Hand Side