MCQ
$\int \frac{1}{\cos x-\cos ^2 x} \cdot d x=$
- A$\log (\operatorname{cosec} x-\cot x)+\tan \left(\frac{x}{2}\right)+c$
- Bsin 2x – cos x + c
- ✓$\log (\sec x+\tan x)-\cot \left(\frac{x}{2}\right)+c$
- Dcos 2x – sin x + c
Hint : $\int \frac{1}{\cos x-\cos ^2 x} d x$
$=\int \frac{1}{\cos x(1-\cos x)} d x$
$=\int \frac{(1-\cos x)+\cos x}{\cos x(1-\cos x)} d x$
$=\int\left[\sec x+\frac{1}{2} \operatorname{cosec}^2\left(\frac{x}{2}\right)\right] d x$
$=\log |\sec x+\tan x|+\frac{1}{2} \frac{\left(-\cot \frac{x}{2}\right)}{1 / 2}+c$
$=\log |\sec x+\tan x|-\cot \left(\frac{x}{2}\right)+c$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to retail store. Then the probability that the store will receive at most one defective bulb is