Question

If cot $\theta =\frac{1}{\sqrt{3}}$,show that $\frac{1-co{s}^2\theta }{2-si{n}^2\theta }=\frac{3}{5}$

Answer 1

Cot x = $\frac{1}{\surd 3}$
x = 60 degrees

cos (x) = cos 60 = $\frac{1}{2}$
sin x = sin 60 = $\frac{\surd 3}{2}$

1 - cos² x = 1 - $\frac{1}{4}$ = $\frac{3}{4}$
2 - sin²x = 2 - $\frac{3}{4}$ = $\frac{5}{4}$
$\frac{1-co{s}^2\theta }{2-si{n}^2\theta }=\frac{3}{5}$