Question

If $\int \frac{dx}{{\cos }^{3}x\sqrt{\sin 2x}}=a({\tan }^{2}x+b)\sqrt{\tan x}+c$, then?

• A. $a=\frac{\sqrt{2}}{5},b=\frac{1}{\sqrt{5}}$
• B. $a=\sqrt{2},b=1$
• C. $a=\frac{\sqrt{2}}{5},b=\frac{-1}{5}$
• D. $a=\frac{\sqrt{2}}{5},b=\sqrt{5}$

Answer 1

The correct option is B $a=\sqrt{2},b=1$

Comparing both side,we get

$a=\frac{\sqrt{2}}{5}$,

$b=\sqrt{5}$