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# How do you verify the identity: cos^{2}x − sin^{2}x = 1 − 2sin^{2}x

Trigonometric identities are equations that relate different trigonometric functions using different mathematical operations.

## Answer: The identity cos^{2}x − sin^{2}x = 1 − 2sin^{2}x is verified.

Let's look into the steps below to prove it.

## Explanation:

To prove: cos^{2}x − sin^{2}x = 1 − 2sin^{2}x

LHS = cos^{2}x − sin^{2}x

According to the trigonometric identity we know that,

cos^{2}x + sin^{2}x = 1

⇒ cos^{2}x = 1 - sin^{2}x

Thus, substituting the value of cos^{2}x in the LHS we get,

(1 - sin^{2}x) - sin^{2}x

⇒ 1 - 2sin^{2}x = RHS

### Thus, the identity cos^{2}x − sin^{2}x = 1 − 2sin^{2}x is verified.

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