Question

The value of $\int \frac{1}{si{n}^{2}xco{s}^{2}x}dx$ is

• A. tan x + cot x
• B. tan x - cot x
• C. sin x + cos x
• D. sin x - cos x

Answer 1

The correct option is B tan x - cot x

$\int \frac{1}{si{n}^{2}xco{s}^{2}x}dx=\int \left(\frac{si{n}^{2}x+co{s}^{2}x}{si{n}^{2}x.co{s}^{2}x}\right)dx$

$=\int \frac{si{n}^{2}x}{si{n}^{2}xco{s}^{2}x}dx+\int \frac{co{s}^{2}x}{si{n}^{2}xco{s}^{2}x}dx$

$=\int \frac{1}{co{s}^{2}x}dx+\int \frac{1}{si{n}^{2}x}dx$

$=se{c}^{2}xdx+\int cose{c}^{2}xdx=tanx-cotx$