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NCERT Class XII Mathematics Chapter - - Solutions

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Choose the correct answers in Exercises 269 to 272.
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Question : 270 of 271
Marks: +1, -0
∫cos⁡2x(sin⁡x+cos⁡x)2dx\int\frac{\cos 2x}{(\sin x+\cos x)^2}dx is equal to
Solution:  
Let I=∫cos⁡2x(sin⁡x+cos⁡x)2dxI=\int\frac{\cos 2x}{(\sin x+\cos x)^2}dx
=∫cos⁡2x−sin⁡2x(sin⁡x+cos⁡x)2dx= \int\frac{\cos^2x-\sin^2x}{(\sin x+\cos x)^2}dx
=∫cos⁡x−sin⁡xsin⁡x+cos⁡xdx= \int\frac{\cos x-\sin x}{\sin x+\cos x}dx
=log⁡∣sin⁡x+cos⁡x∣+C=\log|\sin x+\cos x|+C
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