AP EAMCET · Maths · Definite Integration
\(\int_0^{\frac{\pi}{2}} \frac{\cos x d x}{\sqrt{1+\cos x \sin x}}=\)
- A \(\sqrt{2} \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)
- B \(\frac{1}{\sqrt{2}} \sin ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)
- C \(\sqrt{2} \sin ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)
- D \(\sqrt{2} \sin ^{-1}(\sqrt{3})\)
Answer & Solution
Correct Answer
(C) \(\sqrt{2} \sin ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)
Step-by-step Solution
Detailed explanation
\(\int_0^{\frac{\pi}{2}} \frac{\cos x d x}{\sqrt{1+\cos x \sin x}}\) \(I=\int_0^{\frac{\pi}{2}} \frac{\cos \left(\frac{\pi}{2}-x\right)}{\sqrt{1+\cos \left(\frac{\pi}{2}-x\right) \sin \left(\frac{\pi}{2}-x\right)}} d x\) On adding Eqs. (i) and (ii), we get…
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