Question

If x is in quadrant I and sinx-cosx=1/3, then the value of sinx+cosx is…

A)4/3 B)sqrt17/3 C)-4/9

Answer 1

(sinx-cosx)^2 = 1 - 2sinx cosx = 1/9

so sin2x = 8/9
(sinx-cosx)(sinx+cosx) = sin^2x - cos^2x = -cos2x
cos^2(2x) = 1 - 64/81 = 17/81
sinx+cosx = (√17/9)/(1/3) = √17/3