Question

$\int \frac{1}{si{n}^{2}xco{s}^{2}x}dx$

Answer 1

$\int \frac{1}{si{n}^{2}x.co{s}^{2}x}dx\Rightarrow si{n}^{2}x.co{s}^{2}x$ $sin2x=2sinx.cosx$

$=(sinx.cosx{)}^2$ $\frac{1}{2}sin2x=sinx.cosx$

$=(\frac{1}{2}sin2x{)}^2$

$=\frac{1}{4}si{n}^{2}2x$

$=\int \frac{1}{\frac{1}{4}si{n}^{2}2x}dx$

$=\int (\frac{1}{4}si{n}^{2}2x{)}^{-1}dx$

$=\int 4cose{c}^{2}2x.dx$ $\int cose{c}^{2}x=-cotx$

$=-4cot2x\times \frac{1}{2}+c$

$=-2cot2x+c$