Question

Choose the correct answer
$\int \frac{dx}{si{n}^{2}xco{s}^{2}x}$ is equal to
(a)tan x+cot x +C
(b)tan x-cot x+C
(c)tan xcot x+C
(d)tan x-cot 2x+C

Answer 1

$\int \frac{dx}{si{n}^{2}xco{s}^{2}x}=\int \frac{si{n}^{2}x+co{s}^{2}x}{si{n}^{2}x.co{s}^{2}x}dx[\therefore si{n}^{2}x+co{s}^{2}x=1]=\int \frac{si{n}^{2}x}{si{n}^{2}x.co{s}^{2}x}dx+\int \frac{co{s}^{2}x}{si{n}^{2}x.co{s}^{2}x}dx=\int \frac{1}{co{s}^{2}x}dx+\int \frac{1}{si{n}^{2}x}dx=\int se{c}^{2}xdx+\int cose{c}^{2}xdx=tanx-cotx+C$
Hence, (b) is the correct option.