Question

please answer my question

Answer 1

I am taking theta as x becaus there is no theta symbol in my phone.

(sinx-2sin³x)/(2cos³x-cosx)

=(sinx(1-2sin²x))/(cosx(2cos²x-1))

=(sinxcos2x)/(cosxcos2x)

=sinx/cosx

=tanx

Thus LHS=RHS proved

Answer 2

$Here \: is \: the \: answer \: of \: your \: question$

sin theta - 2sin³ theta / 2cos³ theta - cos theta = tan theta

Now, take L.H.S

= sin theta - 2sin³ theta
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2 cos³ theta - cos theta

= sin theta (1 - 2sin² theta)
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cos theta (2cos² theta - 1)

= sin theta [1 - 2(1 - cos² theta)]
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cos theta (2cos² theta - 1)

As, sin²theta = 1 - cos²theta

= sin theta ( 2cos² theta - 1)
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cos theta (2cos² theta -1)

(2cos² theta - 1) / (2cos² theta - 1)

Cancel out by dividing and 1 came.

So,

= sin theta / cos theta = tan theta

$\textbf{tan theta = tan theta}$

L.H.S = R.H.S

Hence, proved
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