Question

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

Answer 1

Refer to the details given in Explanation.

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.