Question

If $\sin \theta +7\cos \theta =5$, then $\tan \frac{\theta }{2}$ is a root of the equation

• A. $x^2-6x+1=0$
• B. $6x^2-x-1=0$
• C. $6x^2+x+1=0$
• D. $x^2-x+6=0$

Answer 1

Answer: (B)

Let $x=\tan \frac{\theta }{2}$
$\sin \theta +7\cos \theta =5$
$\Rightarrow \frac{2x}{1+x^2}+\frac{7\left(1-x^2\right)}{1+x^2}=5$
$\Rightarrow 6x^2-x-1=0$