# Is this equation an identity? Cos²y-Sin²y=Sin(2y)

Mar 31, 2018

No. See below.

#### Explanation:

No. Regardless of how we try to simplify the left side, the identity will not hold true.

The following are identities:

$\sin \left(2 y\right) = 2 \sin y \cos y$
$\cos \left(2 y\right) = {\cos}^{2} y - {\sin}^{2} y$

So, the equation wrongly sets two completely different trigonometric identities equal.