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

1 Answer
Mar 22, 2018

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.