JEE Main 2022 (26 Jul, Shift 2) Maths Q19: Integrals

Question

The integral $\int\frac{\left(1-\frac{1}{\sqrt{3}}\right)(\cos x-\sin x)}{\left(1+\frac{2}{\sqrt{3}}\sin 2x\right)}dx$ is equal to

Accepted Answer

Option 1: $\frac{1}{2}\log_e\left|\frac{	an\left(\frac{x}{2}+\frac{\pi}{12}ight)}{	an\left(\frac{x}{2}+\frac{\pi}{6}ight)}ight|+C$

Answer

$\frac{1}{2}\log_e\left|\frac{	an\left(\frac{x}{2}+\frac{\pi}{12}ight)}{	an\left(\frac{x}{2}+\frac{\pi}{6}ight)}ight|+C$

Answer

$\frac{1}{2}\log_e\left|\frac{	an\left(\frac{x}{2}+\frac{\pi}{6}ight)}{	an\left(\frac{x}{2}+\frac{\pi}{3}ight)}ight|+C$

Answer

$\log_e\left|\frac{	an\left(\frac{x}{2}+\frac{\pi}{6}ight)}{	an\left(\frac{x}{2}+\frac{\pi}{12}ight)}ight|+C$

Answer

$\frac{1}{2}\log_e\left|\frac{	an\left(\frac{x}{2}-\frac{\pi}{12}ight)}{	an\left(\frac{x}{2}-\frac{\pi}{6}ight)}ight|+C$

JEE Main 26 July 2022, Shift 2, Maths Q19