MCQ
If $\angle A = {90^o}$ in the triangle ABC, then ${\tan ^{ - 1}}\left( {\frac{c}{{a + b}}} \right) + {\tan ^{ - 1}}\left( {\frac{b}{{a + c}}} \right) = $
- A$0$
- B$1$
- ✓$\pi /4$
- D$\pi /6$
✓
Answer
Correct option: C.
$\pi /4$
c
(c) $\angle A = {90^o}$
(c) $\angle A = {90^o}$
${\tan ^{ - 1}}\left( {\frac{c}{{a + b}}} \right) + {\tan ^{ - 1}}\left( {\frac{b}{{a + c}}} \right)$
$ = {\tan ^{ - 1}}\left[ {\frac{{\frac{c}{{a + b}} + \frac{b}{{a + c}}}}{{1 - \left( {\frac{c}{{a + b}}} \right)\left( {\frac{b}{{a + c}}} \right)}}} \right]$
$ = {\tan ^{ - 1}}\left[ {\frac{{ca + {c^2} + ab + {b^2}}}{{{a^2} + ab + ca + bc - bc}}} \right]$
$ = {\tan ^{ - 1}}\left[ {\frac{{{a^2} + ab + ca}}{{{a^2} + ab + ca}}} \right]$
$ = {\tan ^{ - 1}}(1) = \frac{\pi }{4}$.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Let $(\mathrm{x}, \mathrm{y})$ be such that
→$\sin ^{-1}(a x)+\cos ^{-1}(y)+\cos ^{-1}(b x y)=\frac{\pi}{2} .$
Match the statements in Column $I$ with the statements in Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
| Column $I$ | Column $II$ |
| $(A)$ If $a=1$ and $b=0$, then ( $x, y$ ) | $(p)$ lies on the circle $x^2+y^2=1$ |
| $(B)$ If $a=1$ and $b=1$, then $(x, y)$ | $(q)$ lies on $\left(x^2-1\right)\left(y^2-1\right)=0$ |
| $(C)$ If $a=1$ and $b=2$, then ( $x, y)$ | $(r)$ lies on $y=x$ |
| $(D)$ If $a=2$ and $b=2$, then $(x, y)$ | $(s)$ lies on $\left(4 x^2-1\right)\left(y^2-1\right)=0$ |
Consider three vectors $\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}, \overrightarrow{\mathrm{c}}$. Let $|\overrightarrow{\mathrm{a}}|=2,|\overrightarrow{\mathrm{b}}|=3$ and $\overrightarrow{\mathrm{a}}=\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}$. If $\alpha \in\left[0, \frac{\pi}{3}\right]$ is the angle between the vectors $\vec{b}$ and $\vec{c}$, then the minimum value of $27|\overrightarrow{c}-\overrightarrow{a}|^2$ is equal to :
→The equations of the tangents drawn from the origin to the circle ${x^2} + {y^2} - 2rx - 2hy + {h^2} = 0$ are
→The area (in sq. units) of the region $\left\{ {x \in R:x \ge } \right.0,\,y \ge 0,\,y \ge x - 2\,and\,y \le \sqrt x \} \,,\,$ is
→If $A = \left[ {\begin{array}{*{20}{c}}1&2&1\\0&1&{ - 1}\\3&{ - 1}&1\end{array}} \right]$, then
→If a coin be tossed $n$ times then probability that the head comes odd times is
→Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is
The distance of the point $({x_1},{y_1},{z_1})$ from the line $\frac{{x - {x_2}}}{l} = \frac{{y - {y_2}}}{m} = \frac{{z - {z_2}}}{n}$, where $l,m, n$ are the direction cosines of the line, is given by:
→The curve for which the intercept cut off by any tangent on $y-$ axis is proportional to the square of the ordinate of the point of tangency is (where $c_1$ and $c_2$ are arbitrary constants)
→If $x = \sec \theta + \tan \theta ,$ then $x + \frac{1}{x} = $
→