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

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Answer 1 · 2018-03-22T03:41:12

See Below.

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.