Question

The angle $\theta$ whose cosine is equal to its tangent is given by $\sin \theta =n\sin {18}^o$. Find the value of n.

Answer 1

$\tan \theta =\cos \theta ⟹\sin \theta ={\cos }^2\theta ⟹\sin \theta =1-{\sin }^2\theta ⟹\sin \theta =\frac{-1+\sqrt{5}}{2}$

$\sin {18}^{\circ }=\frac{-1+\sqrt{5}}{4}⟹n=\frac{1}{2}$