Question

If sec$\theta$ = 1 $\frac{1}{4}$, then tan $\frac{\theta }{2}$ =

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Given that sec$\theta$ = $\frac{5}{4}$

sec$\theta$ = $\frac{1+ta{n}^2\left(\frac{\theta }{2}\right)}{1-ta{n}^2\left(\frac{\theta }{2}\right)}$ $\Rightarrow$ $\frac{5}{4}$ = $\frac{1+ta{n}^2\left(\frac{\theta }{2}\right)}{1-ta{n}^2\left(\frac{\theta }{2}\right)}$

$\Rightarrow$ $5-5ta{n}^2\left(\frac{\theta }{2}\right)=4+4ta{n}^2\left(\frac{\theta }{2}\right)$

$\Rightarrow$ $9ta{n}^2\left(\frac{\theta }{2}\right)$ = 1 $\Rightarrow$ $tan\left(\frac{\theta }{2}\right)$ = $\frac{1}{3}$.