If b = a ( + 2 ), then a + b a - b = - Vidyadip

MCQ

If $b\sin \alpha = a\sin (\alpha + 2\beta ),$ then $\frac{{a + b}}{{a - b}} = $

A
$\frac{{\tan \beta }}{{\tan (\alpha + \beta )}}$
B
$\frac{{\cot \beta }}{{\cot (\alpha - \beta )}}$
✓
$\frac{{ - \cot \beta }}{{\cot (\alpha + \beta )}}$
D
$\frac{{\cot \beta }}{{\cot (\alpha + \beta )}}$

✓

Answer

Correct option: C.

$\frac{{ - \cot \beta }}{{\cot (\alpha + \beta )}}$

c
(c) We have $b\,\sin \,\alpha = a\,\sin \,(\alpha + 2\beta )\, $

$\Rightarrow \,\frac{a}{b} = \frac{{\sin \,\alpha }}{{\sin \,(\alpha + 2\beta )}}$

$ \Rightarrow \,\,\frac{{a + b}}{{a - b}} = \frac{{\sin \,\alpha + \sin \,(\alpha + 2\beta )}}{{\sin \,\alpha - \sin \,(\alpha + 2\beta )}} $

$= \frac{{2\,\sin \,(\alpha + \beta )\,\cos \,\beta }}{{ - 2\,\cos \,(\alpha + \beta )\,\sin \,\beta }}$

$ = - \tan \,(\alpha + \beta )\,\cot \,\beta $

$= - \frac{{\cot \beta }}{{\cot \,(\alpha + \beta )}}$.

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 "M.C.Q (1 Marks)" from STD 11 - 3. trignometrical ratios,functions and identities→STD 11 - 3. trignometrical ratios,functions and identities — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

From the point$ C(0,\lambda )$ two tangents are drawn to ellipse $x^2\ +\ 2y^2\ = 4$ cutting major axis at $A$ and $B$. If area of $\Delta$ $ABC$ is minimum, then value of $\lambda$ is-

Let $\alpha $ and $\beta $ be integers satisfying $0 < \beta < \alpha $ .Let $P\left( {\alpha ,\beta } \right),Q$ be the reflection of $P$ in the line $y = x, R$ be the reflection of $Q$ in the $y-$ axis, $S$ be the reflection of $R$ in the $x-$ axis and $T$ be the reflection of $S$ in the $y-$ axis. If the area of convex pentagon $PQRST$ is $187\ sq. units$ , then value of $\alpha + {\beta ^2}$ is

Coefficient of ${x^2}$ in the expansion of ${\left( {x - \frac{1}{{2x}}} \right)^8}$ is

The origin and the points where the line $L_1$ intersect the $x$ -axis and $y$ -axis are vertices of right angled triangle $T$ whose area is $8$. Also the line $L_1$ is perpendicular to line $L_2$ : $4x -y = 3$, then perimeter of triangle $T$ is -

If slope of a line is positive then its inclination is:

If the variance of observations ${x_1},\,{x_2},\,......{x_n}$ is ${\sigma ^2}$, then the variance of $a{x_1},\,a{x_2}.......,\,a{x_n}$, $\alpha \ne 0$ is

If $a_1 , a_2, a_3, . . . . , a_n, ....$ are in $A.P.$ such that $a_4 - a_7 + a_{10}\, = m$, then the sum of first $13$ terms of this $A.P.$, is .............. $\mathrm{m}$

Let complex numbers $\alpha$ and $\frac{1}{\bar{\alpha}}$ lies on circles $\left(x-x_0\right)^2+\left(y-y_0\right)^2=r^2$ and $\left(x-x_0\right)^2+\left(y-y_0\right)^2=4 r^2$, respectively. If $z_0=x_0+$ iy, satisfies the equation $2 \mid z_0{ }^2= r ^2+2$, then $|\alpha|=$

The area of the curve ${x^2} + {y^2} = 2ax$ is

If the points $(-2,-5), \,(2,-2)\,, (8,a)$ are collinear, then the value of a is