Question

Find an acute angle θ when (cosθ − sin θ)/(cosθ+sin θ) =(1−√3)/(1+√3)

Answer 1

(cosθ − sinθ)/(cosθ+sinθ) = (1−√3)/(1+√3)

Dividing the numerator and denominator of LHS by cosθ, we get 

1 − tanθ/(1+tanθ) = 1−√3 /(1+√3) 

Which on simplification (or comparison) gives tanθ = √3 

Or θ= 60°