Question

Choose the correct answers from the alternatives given.
If tan $\theta (\frac{\pi }{2}-\frac{\theta }{2})=\sqrt{3}$ the value of cos $\theta$ is

• A. 0
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{1}{2}$
• D. 1

Answer 1

The correct option is C $\frac{1}{2}$

$tan\theta (\frac{\pi }{2}-\frac{\theta }{2})=\sqrt{3}$
$tan(\frac{\pi }{2}-\frac{\theta }{2})=tan\frac{\pi }{3}$
$\frac{\pi }{2}-\frac{\theta }{2}=\frac{\pi }{3}\Rightarrow \frac{\theta }{2}=\frac{\pi }{2}-\frac{\pi }{3}=\frac{\pi }{6}$
$\theta ={60}^{\circ }$
$cos\theta =cos{60}^{\circ }=\frac{1}{2}$