∫cos⁡x−sin⁡x8−sin⁡2xdx=asin−1⁡sin⁡x+cos⁡xb+c where c is constant of integration, then the ordered pair a,b=

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-1,3

3,1

1,-3

1,3

answer is D.

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Detailed Solution

∫cos⁡x−sin⁡x8−sin⁡2xdx=∫cos⁡x−sin⁡x9−(sin⁡x+cos⁡x)2dx let sin⁡x+cos⁡x=t(cos⁡x−sin⁡x)dx=dt=∫dt9−t2=sin−1⁡t3+c=sin−1⁡sin⁡x+cos⁡x3+cHence, a,b=1,3