Question

prove that (sin A+cos A)^2+( sinA -cos A)^2 =2

Answer 1

We know that (a+b)^2 + (a-b)^2= 2(a^2 + b^2)

Hence,

LHS = (sinA+cosA) ^2 + (sinA-cosA) ^2

= 2(sin square A + cos square A)

= 2 (1) = 2 = RHS.

Since sin squareA + cos square A = 1