How do you verify the identity: cos²x − sin²x = 1 − 2sin²x 

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

Answer: The identity cos²x − sin²x = 1 − 2sin²x is verified.

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

Explanation:

To prove: cos²x − sin²x = 1 − 2sin²x

LHS = cos²x − sin²x

According to the trigonometric identity we know that,

cos²x + sin²x = 1

⇒ cos²x = 1 - sin²x

Thus, substituting the value of cos²x in the LHS we get,

(1 - sin²x) - sin²x

⇒ 1 - 2sin²x = RHS

Thus, the identity cos²x − sin²x = 1 − 2sin²x is verified.