MCQ
${\tan ^{ - 1}}\frac{{a - b}}{{1 + ab}} + {\tan ^{ - 1}}\frac{{b - c}}{{1 + bc}} = $
- A${\tan ^{ - 1}}a - {\tan ^{ - 1}}b$
- ✓${\tan ^{ - 1}}a - {\tan ^{ - 1}}c$
- C${\tan ^{ - 1}}b - {\tan ^{ - 1}}c$
- D${\tan ^{ - 1}}c - {\tan ^{ - 1}}a$
$ = {\tan ^{ - 1}}(a) - {\tan ^{ - 1}}(b) + {\tan ^{ - 1}}(b) - {\tan ^{ - 1}}(c)$
$ = {\tan ^{ - 1}}(a) - {\tan ^{ - 1}}(c)$.
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(There are two questions based on $PARAGRAPH "II"$, the question given below is one of them)
($1$) The value of $2 \int^{\frac{\pi}{2}} f(x) g(x) d x-\int^{\frac{\pi}{2}} g(x) d x$ us
($2$) The value of $\frac{16}{\pi^3} \int_0^{\frac{\pi}{2}} f(x) g(x) d x$ is
Give the answer or quetion ($1$) and ($2$)