Question

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

Answer 1

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

`(sin y + cos y)^2 = sin^2y + cos^2 y`

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

`(sin y + cos y)^2 = (sin y)^2 + 2*siny*cosy + (cos y)^2 = sin^2y + 2sinycosy + cos^2y`

But The Right Hand Side is equal to `sin^2y + cos^2y`.

So, L.H.S `!=` R.H.S

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