we are given that cos theta+cos square theta=1, then find the value of sin theta+sin square theta?

Let's call the angle A than θ.

cosA + cos²A = 1

cosA + cos²A  -1 = 0

cosA = 1-  cos²A 

cosA = sin²A

The roots of this quadratic equation,

cosA = (-1±√5)/2 = sin²A

sinA = [(-1±√5)/2]^1/2

Hence sinA + sin²A = (-1±√5)/2 + [(-1±√5)/2]^1/2

regards,

Team,

TopperLearning.