$\int \frac{d x}{(\sin x)(\cos x)}$ is equal to
$\int \frac{d x}{(\sin x)(\cos x)}$ is equal to
- $\log |\sin x|+c$
- $\log |\cos x|+c$
- $\log |\tan x|+c$
- $\log |\operatorname{cosec} x|+c$
Solution
$
\text { Let } \begin{aligned}
I & =\int \frac{d x}{\sin x \cos x} \\
I & =\int \frac{\sec ^2 x d x}{\tan x}
\end{aligned}
$
Put $\tan x=t$
$
\begin{array}{ll}
\Rightarrow & \sec ^2 x d x=d t \\
\therefore & I=\int \frac{d t}{t}=\log t+c \\
& I=\log |\tan x|+c
\end{array}
$
Asked in: AP EAMCET 2021 (25 Aug Shift 1)
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