Question

\(\int \frac{dx}{\sin^2 x \cos^2 x}\) equals

• A. tan x + cot x +C
• B. tan x - cot x +C
• C. tan x cot x +C
• D. tan x-cot 2x +C

Answer 1

The Correct Option is B

Let\(I=\int \frac{dx}{\sin^2 x \cos^2 x}\)

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

= \(\int \frac{\sin^2 x+ \cos^2 x}{\sin^2 x \cos^2 x}dx\)

= \(\int \frac{\sin^2x}{\sin^2x\cos^2 x}dx+\int\frac{\cos^2 x}{\sin^2x\cos^2x}dx\)

= \(\int \sec^2 xdx+\int\cosec^2 xdx\)

= \(\tan x -\cot x+C\)

Hence, the correct answer is B.