How do you prove $cos(x)tan(X) + sin(x)cot(x) = sin(x) + cos^2(x)$ ?

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Answer 1 · 2018-07-25T06:35:07

Please see below.

We know that,

$diamondtan theta=sintheta/cos theta and cottheta=costheta/sintheta$

Given that

$cosxtancolor(red)(x)+sinxcotx=sinx+color(red)(cos^2x$

We take ,

$LHS=cosxtanx+sinxcotx$

$color(white)(LHS)=cosx(sinx/cosx)+sinx(cosx/sinx)$

$color(white)(LHS)=sinx+cosx!=sinx+cos^2x$

So, $LHS!=RHS$

Hence, we cannot prove the above result.
Please check your question.

How do you prove cos(x)tan(X) + sin(x)cot(x) = sin(x) + cos^2(x)cos(x)tan(X) + sin(x)cot(x) = sin(x) + cos^2(x)?