# How do I this equation is not an identity? Write explanation in paragraph form (Siny+Cosy)²=Sin²y+Cos²y

Mar 22, 2018

See Below.

#### Explanation:

An Identity is an algebraical expression with variables, where the expression remains true, no matter what the values variables take.

So, Here The expression is

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

The Left Hand Side, When expanded, is equal to:

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

But The Right Hand Side is equal to ${\sin}^{2} y + {\cos}^{2} y$.

So, L.H.S $\ne$ R.H.S

So, This can't be an identity in any cost.