Question

If x = sin A + cos A and y = sin A - Cos A, find the value of x² + y²​

Answer 1

Given: $x=sinA+cosA$

             $y = sinA-cosA$

To find: $x^{2} +y^{2}$

Step-by-step explanation:

$x^{2} +y^2$

⇒$(sinA+cosA)^2+(sinA-cosA)^2$

Using the identity, $(a+b)^2= a^2+b^2+2ab$

                                 $(a-b)^2= a^2+b^2-2ab$

⇒ $sin^2A + cos^2A+2sinAcosA + sin^2A+cos^2A - 2sinAcosA$

   ∵ $Sin^2x+Cos^2x= 1$

⇒ $1+1$

⇒$2$