Question

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

Answer 1

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