The value of 2 - $\sqrt{\frac{cotθ+cosθ}{cotθ-cosθ}}$ when 0o < θ < 90o is equal to :
Answer & explanation
Correct answer: option 3
2 - $\sqrt{\frac{cotθ+cosθ}{cotθ-cosθ}}$
= 2 - $\sqrt{\frac{1+sinθ}{1-sinθ}} × \sqrt{\frac{1+sinθ}{1+sinθ}}$
= 2 - $\sqrt{\frac{(1+sinθ)2}{12-sin2θ}} $
= 2 - $\sqrt{\frac{(1+sinθ)2}{cos2θ}} $
= 2 - secθ - tanθ