TS EAMCET · Maths · Indefinite Integration
\(\int(\sqrt{\tan x}+\sqrt{\cot x}) d x=\)
- A \(\sqrt{2} \sin ^{-1}(\sin x+\cos x)+c\)
- B \(\sqrt{2} \cos ^{-1}(\sin x+\cos x)+c\)
- C \(\sqrt{2} \cos ^{-1}(\sin x-\cos x)+c\)
- D \(\sqrt{2} \sin ^{-1}(\sin x-\cos x)+c\)
Answer & Solution
Correct Answer
(D) \(\sqrt{2} \sin ^{-1}(\sin x-\cos x)+c\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} & \int(\sqrt{\tan x}+\sqrt{\cot x}) d x \\ & =\int\left(\sqrt{\frac{\sin x}{\cos x}}+\sqrt{\frac{\cos x}{\sin x}}\right) d x=\int \frac{\sin x+\cos x}{\sqrt{\sin x \cos x}} \end{aligned} \] multiply and divide by \(\sqrt{2}\),…
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