MHT CET · Maths · Definite Integration
\( \int_{0}^{\frac{\pi}{2}} \frac{d x}{1+\cos x}= \)
- A -2
- B 2
- C 1
- D -1
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
\({\text{Let}}1 =\int_{0}^{\frac{\pi}{2}} \frac{\mathrm{dx}}{1+\cos \mathrm{x}}=\int_{0}^{\frac{\pi}{2}} \frac{\mathrm{dx}}{2 \cos ^{2} \frac{\mathrm{x}}{2}}=\) \(\frac{1}{2} \int_{0}^{\frac{\pi}{2}} \sec ^{2} \frac{\mathrm{x}}{2} \mathrm{dx} \)
\( =\frac{1}{2}\left[\frac{\tan \frac{\mathrm{x}}{2}}{\left(\frac{1}{2}\right)}\right]_{0}^{\frac{\pi}{2}}=\tan \frac{\pi}{4}-\tan 0=1-0=1 \)
\( =\frac{1}{2}\left[\frac{\tan \frac{\mathrm{x}}{2}}{\left(\frac{1}{2}\right)}\right]_{0}^{\frac{\pi}{2}}=\tan \frac{\pi}{4}-\tan 0=1-0=1 \)
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