Question

integrade dx/cosx-✓3sinx​

Answer 1

Step-by-step explanation:

We have,

$\int \frac{dx}{ \cos(x) - \sqrt{3} \sin(x) }$

$= \int \frac{dx}{2( \frac{1}{2} \cos(x) - \frac{ \sqrt{3} }{2} \sin(x) )}$

$= \int \frac{dx}{2( \sin( \frac{\pi}{6} ) \cos(x) - \cos( \frac{\pi}{6} ) \sin(x) ) }$

$= \frac{1}{2} \int \frac{dx}{ \sin( \frac{\pi}{6} - x ) }$

$= \frac{1}{2} \int \cosec( \frac{\pi}{6} - x)dx$

$= - \frac{1}{2} ln | \tan( \frac{\pi}{12} - \frac{x}{2} ) | + c$

$= - ln\sqrt{ \tan(\frac{\pi}{12} - \frac{x}{2} ) } + c$