Question

$ \int \frac{\sin^{2}x-\cos^{2}x}{\sin^{2}x\cos^{2}x}dx $ is equal to

• A. $ \cot\, x - \tan\, x + C $
• B. $ \tan\, x - \cot\, x + C $
• C. $\tan\, x - \cos ec \,x + C $
• D. $ \tan\, x + \sec \,x + C $

Answer 1

Answer: (B)

$\int \frac{\sin ^{2} x-\cos ^{2} x}{\sin ^{2} x \cos ^{2} x} d x $
$=\int\left(\frac{1}{\cos ^{2} x}-\frac{1}{\sin ^{2} x}\right) d x $
$=\int\left(\sec ^{2} x-\text{cosec}^{2} x\right)$
$=\tan x+\cot x+C $