Mathematics: Directions: verify whether the identity is true while only working on one side of the equation. 1 - 2sin^2(x) = 2cos^2(x) - 1

X2 + x - 6 = 0. Your answer should be {2, -3}. ...

Directions: verify whether the identity is true while

arianabryant54

09.01.2022

Proved that $1 - 2\sin ^{2}x = 2\cos ^{2} x - 1$ .

Step-by-step 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)

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