Maths · Integral as an anti-derivative
If }{\log (\sin \boldsymbol{x})} \boldsymbol{d} \boldsymbol{x}=\log [\log \sin \
If \( \int \frac{\boldsymbol{f}(\boldsymbol{x})}{\log (\sin \boldsymbol{x})} \boldsymbol{d} \boldsymbol{x}=\log [\log \sin \boldsymbol{x}]+\boldsymbol{c} \) \( \operatorname{then} f(x)=\dots \)
- A. \( \cot x \)
- B. \( \tan x \)
- C. \sec x \)
- D. \( \operatorname{cosec} x \)
Step-by-step solution
Differentiate both sides: left side gives f(x)/log(sin x) by FTC, right side gives cot x / log(sin x). Equating yields f(x) = cot x.