Evaluate: ∫ 2cosx/sin^2x dx

Question

Evaluate: ∫ \(\frac{2\ cos\ x}{sin^2 x} \ dx\)

Answer 1

∫ \(\frac{2\ cos\ x}{sin^2 x} dx\) dx = 2 ∫ \(\frac{1}{sin\ x}. \frac{cos\ x}{sin\ x} \ dx\)

= 2 ∫cosec x cot x dx

= 2 (- cosec x) + C

= - \(\frac{2}{sin\ x} + c\)