Choose the correct option from given four options : 2x- 2 - dx is… - Vidyadip

MCQ

Choose the correct option from given four options : $\int\frac{\cos2\text{x}-\cos2\theta}{\cos\text{x}-\cos\theta}\text{dx}$ is equal to :

✓
$2(\sin+\text{x}\cos\theta)+\text{C}$
B
$2(\sin-\text{x}\cos\theta)+\text{C}$
C
$2(\sin+2\text{x}\cos\theta)+\text{C}$
D
$2(\sin-2\text{x}\cos\theta)+\text{C}$

✓

Answer

Correct option: A.

$2(\sin+\text{x}\cos\theta)+\text{C}$

Let $\text{I}=\int\frac{\cos2\text{x}-\cos2\theta}{\cos\text{x}-\cos\theta}\text{dx}$
$=\int\frac{\big(2\cos^2\text{x}-1-2\cos^2\theta+1)}{\cos\text{x}-\cos\theta}\text{dx}$
$=2\int\frac{\big(\cos\text{x}+\cos\theta)(\cos\text{x}-\cos\theta)}{\cos\text{x}-\cos\theta}\text{dx}$
$=2\int(\cos\text{x}+\cos\theta)\text{dx}$
$=2(\sin\text{x}+\text{x}\cos\theta)+\text{C}$

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