The value of $1+\sqrt{\frac{\cot \theta+\cos \theta}{\cot \theta-\cos \theta}}$, if $0^{\circ}<\theta<90^{\circ}$, is equal to:
Answer & explanation
Correct answer: option 4
1 + $\sqrt{\frac{cotθ+cosθ}{cotθ-cosθ}}$
=1 + $\sqrt{\frac{1+sinθ}{1-sinθ}} × \sqrt{\frac{1+sinθ}{1+sinθ}}$
= 1 + $\sqrt{\frac{(1+sinθ)2}{12-sin2θ}} $
= 1 + $\sqrt{\frac{(1+sinθ)2}{cos2θ}} $
= 1 + secθ + tanθ