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Integration as Antiderivative

Evaluate: t...

Question

Evaluate: $\frac{tan x}{\frac{{sin}^{3} x}{cos x} + sin x cos x}$

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Solution

$\frac{t a n x}{\frac{s i n^{3} x}{c o s x}} + s i n x c o s x$
$= \frac{t a n x \times c o s x}{s i n^{3} x + s i n x c o s^{2} x}$
$= \frac{\frac{s i n x}{c o s x} \times c o s x}{s i n x (s i n)^{2} x + c o s^{2} x}$
$= \frac{s i n x}{s i n x (1)} = 1.$

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