If A = n B, then n - 1 n + 1 , A + B 2 = - Vidyadip

MCQ

If $\sin A = n\sin B,$ then $\frac{{n - 1}}{{n + 1}}\tan \,\frac{{A + B}}{2} = $

A
$\sin \frac{{A - B}}{2}$
✓
$\tan \frac{{A - B}}{2}$
C
$\cot \frac{{A - B}}{2}$
D
None of these

✓

Answer

Correct option: B.

$\tan \frac{{A - B}}{2}$

b
(b) We have $\sin A = n\sin B \Rightarrow \frac{n}{1} = \frac{{\sin A}}{{\sin B}}$

$ \Rightarrow \frac{{n - 1}}{{n + 1}} = \frac{{\sin A - \sin B}}{{\sin A + \sin B}} $

$= \frac{{2\cos \frac{{A + B}}{2}\sin \frac{{A - B}}{2}}}{{2\sin \frac{{A + B}}{2}\cos \frac{{A - B}}{2}}}$

$ = \tan \frac{{A - B}}{2}\cot \frac{{A + B}}{2}$

$ \Rightarrow \frac{{n - 1}}{{n + 1}}\tan \left( {\frac{{A + B}}{2}} \right) = \tan \frac{{A - B}}{2}$ .

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from 3. trignometrical ratios,functions and identities→3. trignometrical ratios,functions and identities — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The number of diagonals in a polygon of $m$ sides is

A school has four sections of chemistry in class $XII$ having $40, 35, 45$ and $42$ students. The mean marks obtained in chemistry test are $50, 60, 55$ and $45$ respectively for the four sections, the over all average of marks per students is

If $x, y, z \in R^+$ such that $x + y + z = 4$, then maximum possible value of $xyz^2$ is -

A coin is tossed $3$ times by $2$ persons. What is the probability that both get equal number of heads

The circle $x^2+y^2+2 g x+2 f y+c=0$ does not intersect $x$-axis, if:

Let $C_1$ be the circle of radius $1$ with center at the origin. Let $C_2$ be the circle of radius $\mathrm{I}$ with center at the point $A=(4,1)$, where $1<\mathrm{r}<3$. Two distinct common tangents $P Q$ and $S T$ of $C_1$ and $C_2$ are drawn. The tangent $P Q$ touches $C_1$ at $P$ and $C_2$ at $Q$. The tangent $S T$ touches $C_1$ at $S$ and $C_2$ at $T$. Mid points of the line segments $P Q$ and $S T$ are joined to form a line which meets the $x$-axis at a point $B$. If $A B=\sqrt{5}$, then the value of $r^2$ is

If the parabola $y^2=4 a x$ passes through (3, 2) then the length of latus rectum is:

Number of solution$(s)$ of the equation $ln(1 + sin^2x) = 1 -ln(5 + x^2)$ is -

For $n \in N$, let $S _{ n }=\left\{ z \in C :| z -3+2 i |=\frac{ n }{4}\right\}$ and $T _{ n }=\left\{ z \in C :| z -2+3 i |=\frac{1}{ n }\right\}$ Then the number of elements in the set $\left\{ n \in N : S _{ a } \cap T _{ n }=\phi\right\}$ is.

Choose the conclusion of given statements: All scientists working in America are talented. Some Indian scientists are working in America. Therefore, "Some Indian scientists are talented."