Trigonometric Elimination

Question

Eliminate  θ from the pair of equations:

1) x= sin θ + cos θ and y= sin θ - cos θ

Answer:x^2 + y^2 = 2

(Please show working out)

Answer 1

Let "theta" = T

x^2 + y^2 = (sinT + cosT)^2 + (sinT - cosT)^2

= (sinT)^2 + 2sinTcosT + (cosT)^2 + (sinT)^2 - 2sinTcosT + (cosT)^2

= 2(sinT)^2 + 2(cosT)^2

= 2[(sinT)^2 + (cosT)^2] = 2(1) = 2

So, x^2 + y^2 = 2