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  4. If sin θ+7 cos θ=5, then tan (θ/2) is a root of the equation

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

Trigonometric Functions

Solution:

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