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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_0^{\frac{\pi}{2}} \frac{\cos 2 x}{\cos x+\sin x} d x=$
  • A
    -1
  • B
    1
  • ✓
    $0$
  • D
    2
✓

Answer

Correct option: C.
$0$
(C)
$\int_0^{\frac{\pi}{2}} \frac{\cos 2 x}{\cos x+\sin x} d x$
$=\int_0^{\frac{\pi}{2}} \frac{\cos ^2 x-\sin ^2 x}{\cos x+\sin x} d x$
$\begin{array}{l}=\int_0^{\frac{\pi}{2}}(\cos x-\sin x) d x \\ =[\sin x+\cos x]_0^{\pi / 2}=0\end{array}$

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