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CBSE Class 12 Math 2024 All Sets Solved Paper

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Question : 6 of 20
Marks: +1, -0
∫0π2sin⁡x−cos⁡x1+sin⁡xcos⁡xdx\int\limits_{0}^{\frac{\pi}{2}} \frac{\sin x - \cos x}{1 + \sin x \cos x} dx is equal to
Solution:  
Let I=∫0π2sin⁡x−cos⁡x1+sin⁡xcos⁡x    ....(1)I = \int\limits_{0}^{\frac{\pi}{2}} \frac{\sin x - \cos x}{1 + \sin x \cos x} \;\; \text{....(1)}
I=∫0π2sin⁡(π2−x)−cos⁡(π2−x)1+sin⁡(π2−x)cos⁡(π2−x)I = \int\limits_{0}^{\frac{\pi}{2}} \frac{\sin\left(\frac{\pi}{2} - x\right) - \cos\left(\frac{\pi}{2} - x\right)}{1 + \sin\left(\frac{\pi}{2} - x\right) \cos\left(\frac{\pi}{2} - x\right)}
I=∫0π2cos⁡x−sin⁡x1+sin⁡xcos⁡x    ....(2)I = \int\limits_{0}^{\frac{\pi}{2}} \frac{\cos x - \sin x}{1 + \sin x \cos x} \;\; \text{....(2)}
Adding (1) and (2) together, we get
2I = 0
I = 0
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