Question

If ${\theta }_1$ and ${\theta }_2$ are two value lying on [0, 2$\pi$] for which tan$\theta$ = $\lambda$ then tan $\frac{{\theta }_1}{2}$.tan $\frac{{\theta }_2}{2}$ is

• A. 0
• B. -1
• C. 2
• D. 1

Answer 1

The correct option is B

-1

tan$\theta$ = $\lambda$ ⇒ $\frac{2tan\frac{\theta }{2}}{1-ta{n}^2\frac{\theta }{2}}$ = $\lambda$

⇒ $\lambda$ $ta{n}^2$ $\frac{\theta }{2}$ + 2tan $\frac{\theta }{2}$ - $\lambda$ = 0

⇒ tan $\frac{{\theta }_1}{2}$ tan $\frac{{\theta }_2}{2}$ = -1