A) \[-1\]
B) 1
C) 0
D) None of these
Correct Answer: B
Solution :
On integrating both functions, we get \[=\frac{1}{2}\left| \log (1+{{t}^{2}}) \right|_{1/e}^{\tan x}+\left| \left\{ \log t-\frac{1}{2}\log (1+{{t}^{2}}) \right\} \right|_{1/e}^{\cot x}\] \[=\frac{1}{2}\left[ \log {{\sec }^{2}}x-\log \left( 1+\frac{1}{{{e}^{2}}} \right) \right]+\log \cot x-\log \left( \frac{1}{e} \right)\] \[-\frac{1}{2}\left\{ \log (\text{cose}{{\text{c}}^{2}}x)-\log \left( 1+\frac{1}{{{e}^{2}}} \right) \right\}\]\[=-\log \left( \frac{1}{e} \right)=\log e=1\].
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