Question

If $3\sin x+4\cos x=5$, then $6\tan \frac{x}{2}-9{\tan }^2\frac{x}{2}$ is equal to

• A. 0
• B. 1
• C. 3
• D. 4

Answer 1

Answer: (B)

Given, $3\sin x+4\cos x=5$
$\Rightarrow 3\left(\frac{2\tan \frac{x}{2}}{1+{\tan }^2\frac{x}{2}}\right)+4\left(\frac{1-{\tan }^2\frac{x}{2}}{1+{\tan }^2\frac{x}{2}}\right)=5$
$\Rightarrow 6\tan \frac{x}{2}+4-4{\tan }^2\frac{x}{2}=5\left(1+{\tan }^2\frac{x}{2}\right)$
$\Rightarrow 6\tan \frac{x}{2}-9{\tan }^2\frac{x}{2}=1$