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Q.

∫tan⁡xsin⁡xcos⁡xdx is equal to

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a

−2tanx+C

b

2tanx+C

c

2cotx+C

d

−2cotx+C

answer is B.

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Detailed Solution

Let I=∫tan⁡xsin⁡xcos⁡xdx=∫tan⁡xtan⁡xcos2⁡xdxI=∫sec2xdxtanxdxlet     tanx = tsec2⁡xdx=dtI=∫1tdt=2t+C=2tan⁡x+C
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∫tan⁡xsin⁡xcos⁡xdx is equal to