Question

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

Answer 1

Please see below.

Explanation:

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.
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