Question

Verify the identity 6cos^2(x) -3 = 3 - 6sin^2(x)

Answer 1

It is proved that
`6\cos ^(2)x -3 = 3 - 6\sin ^(2) x` .

Explanation:

We already have the identity of x as
`\sin ^(2)x + \cos ^(2)x = 1` .......... (1) .

So, from equation (1) we can write that

`\cos ^(2) x = 1 - \sin ^(2) x`

⇒
`6\cos ^(2) x = 6 - 6 \sin ^(2) x`

⇒
`6\cos ^(2) x -3 = 6 - 6 \sin ^(2)x -3`

⇒
`6\cos ^(2)x -3 = 3 - 6\sin ^(2) x`

Hence, it is proved that
`6\cos ^(2)x -3 = 3 - 6\sin ^(2) x` . (Answer)