Question

Directions: Verify whether the identity is true while only working on one side of the equation.

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

Answer 1

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

Explanation:

We know the following identity as
`\sin ^(2) x + \cos ^(2) x =1` .......... (1) and we commonly use this identity as a formula.

Now, rearranging the identity we get

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

⇒
`2\sin ^(2)x = 2 - 2\cos ^(2) x`

⇒
`- 2\sin ^(2)x = 2\cos ^(2) x - 2`

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

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

Hence, proved that
`1 - 2\sin ^(2)x = 2\cos ^(2) x - 1`. (Answer)