Choose the correct answer in Exercises: ^2x- ^2x ^2x ^2x dx is eq…

MCQ

Choose the correct answer in Exercises:
$\int\frac{\sin^2\text{x}-\cos^2\text{x}}{\sin^2\text{x}\cos^2\text{x}}\text{ dx}$ is equal to

✓
$\tan\text{x}+\cot\text{x}+\text{C}$
B
$\tan\text{x}+\text{cosec x}+\text{C}$
C
$-\tan\text{x}+\cot\text{x}+\text{C}$
D
$\tan\text{x}+\sec\text{x}+\text{C}$

✓

Answer

Correct option: A.

$\tan\text{x}+\cot\text{x}+\text{C}$

$\int\frac{\sin^2\text{x}-\cos^2\text{x}}{\sin^2\text{x}\cos^2\text{x}}\text{ dx}$
$=\int\bigg(\frac{\sin^2\text{x}}{\sin^2\text{x}\cos^2\text{x}}-\frac{\cos^2\text{x}}{\sin^2\text{x}\cos^2\text{x}}\bigg)\text{dx}$
$=\int(\sec^2\text{x}-\text{cosec}^2\text{x})\text{ dx}$
$=\tan\text{x}+\cot\text{x}+\text{C}$
Hence, the correct answer is A.

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