If + =a and - =b then - 2 = - Vidyadip

MCQ

If $\sin\alpha+\sin\beta=\text{a}$ and $\cos\alpha-\cos\beta=\text{b}$ then $\tan\frac{\alpha-\beta}{2}=$

A
$-\frac{\text{a}}{\text{b}}$
B
$-\frac{\text{b}}{\text{a}}$
C
$\sqrt{\text{a}^2+\text{b}^2}$
D
None of these

✓

Answer

$-\frac{\text{b}}{\text{a}}$

Solution:

Given:

$\sin\alpha+\sin\beta=\text{a}$

$\Rightarrow2\sin\frac{\alpha+\beta}{2}\cos\frac{\alpha+\beta}{2}=\text{a}\ .....(1)$

Also,

$\cos\alpha+\cos\beta=\text{b}$

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

On dividing (1) by (2), we get

$\frac{-\cos\frac{\alpha+\beta}{2}}{\sin\frac{\alpha-\beta}{2}}=\frac{\text{a}}{\text{b}}$

$\Rightarrow\frac{-\sin\frac{\alpha+\beta}{2}}{\cos\frac{\alpha-\beta}{2}}=\frac{\text{b}}{\text{a}}$

$\Rightarrow\tan\frac{\alpha-\beta}{2}=-\frac{\text{b}}{\text{a}}$

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 Trigonometric Functions→Trigonometric Functions — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

If equation of line is y = 5x + 10 then find the value of x-intercept made by the line:

The value of $\sin^25^\circ+\sin^210^\circ+\sin^215^\circ+\ ...\ +\sin^285^\circ+\sin^290^\circ$ is:

7
8
9.5
10

A die is rolled, then the probability that a number 1 or 6 may appear is

Differentiate with respect to x x⁴ + 3x² − 2x:

The mean deviation of the numbers 3, 4, 5, 6, 7 from the mean is:

The value of $ \displaystyle \lim _{ \text{x}\rightarrow \text{a} }{ \frac { \sqrt { \text{x-b} } -\sqrt {\text{ a-b} } }{ { \text{x} }^{ 2 }-{ \text{a} }^{ 2 } } } \text{(a > b)}:$

Mark the correct alternative in each of the following:
If $\text{f(x)}=\text{x}\sin\text{x},$ then $\text{f}'\Big(\frac{\text{x}}{2}\Big)=$

Let ${{\omega }_{n}}=\cos \left( \frac{2\pi }{n} \right)+i\,\sin \left( \frac{2\pi }{n} \right)\,,\,{{i}^{2}}=-1$, then $(x+y{{\omega }_{3}}+z{{\omega }_{3}}^{2})$ $(x+y{{\omega }_{3}}^{2}+z{{\omega }_{3}})$ is equal to [AMU 2001]

The vertex of the parabola (y + a)² = 8a (x - a) is

In a $\triangle\text{ABC}$ if A is the point (1, 2) and equations of the median through B and C are respectively x + y = 5 and x = 4, then B is: