How do you solve $cos x - 2sin^2 x = 2cos^2x + cos x -2$ ?

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Answer 1 · 2016-07-20T16:55:18

Refer to the details given in Explanation.

In fact, this is an Identity and not an eqn. to be "solved"

Despite, if we want to consider it as an eqn., its soln. set will clearly be $RR$ .

As regards proving it as an Identity, we have, $cos^2x+sin^2x=1rArr sin^2x=1-cos^2x$

$:.$ The L.H.S. $=cosx-2sin^2x=cosx-2(1-cos^2x)$

$=cosx-2+2cos^2x=$ The R.H.S.

Hence, the Proof.

How do you solve cos x - 2sin^2 x = 2cos^2x + cos x -2cos x - 2sin^2 x = 2cos^2x + cos x -2?