To prove a statement is not an identity find a value that ma

To prove a statement is not an identity, find a value that makes the statement false. Which angle proves (sin A + cos A)^2 = sin^2 A + cos^2 A is not an identity. Pi/4 0 3 pi/2 pi

Solution

(sinA +cosA)^2 = sin^2A +cos^2A

LHS :(sinA +cosA)^2 = sin^2A +cos^2A +2sinAcosA

for A = pi/4 :

:(sinA +cosA)^2 =   1/2 +1/2 + 2(1/sqrt2)(1/sqrt2) = 1+1 =2

RHS sin^2A +cos^2A = (1/sqrt2)^2 +(1/sqrt2)^2 =1

So, LHS is not equal to RHS

OPtion pi/4