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

Correct option is 412(log⁡tan⁡x)2

Questions

The function $f$ whose graph passes through $(π / 4, 0)$
and whose derivative is $\frac{\log (\tan x)}{\sin x \cos x}$ is given by

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(log⁡tan⁡x)2+π4

12(log⁡cos⁡x)2

12(log⁡sin⁡x)2

12(log⁡tan⁡x)2

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detailed solution

Correct option is D

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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The function $f$ whose graph passes through $(π / 4, 0)$
and whose derivative is $\frac{\log (\tan x)}{\sin x \cos x}$ is given by