Q.

The function f whose graph passes through (π/4,0)and whose derivative is log⁡(tan⁡x)sin⁡xcos⁡x is given by

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a

(log⁡tan⁡x)2+π4

b

12(log⁡cos⁡x)2

c

12(log⁡sin⁡x)2

d

12(log⁡tan⁡x)2

answer is D.

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Detailed Solution

f(x)=∫log⁡(tan⁡x)sin⁡xcos⁡x=12(log⁡tan⁡x)2+C0=fπ4=12(log⁡1)2+C⇒C=0
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The function f whose graph passes through (π/4,0)and whose derivative is log⁡(tan⁡x)sin⁡xcos⁡x is given by