Download App

TRIGONOMETRIC FUNCTIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTRIGONOMETRIC FUNCTIONS1 Mark
MCQ
$\text{If}\ \sin\alpha+\sin\beta=\text{a}\text{ and }\cos\alpha-\cos\beta=\text{b},\ \text{than }\tan\frac{\alpha-\beta}{2}=$
  • A
    $-\frac{\text{a}}{\text{b}}$
  • ✓
    $-\frac{\text{b}}{\text{a}}$
  • C
    $\sqrt{\text{a}^2+\text{b}^2}$
  • D
    None of these
✓

Answer

Correct option: B.
$-\frac{\text{b}}{\text{a}}$
Given:
$\sin\alpha+\sin\beta=\text{a}...(\text{i})$
$\cos\alpha-\cos\beta=\text{b}...(\text{ii})$
Dividing (i) by (ii):
$\Rightarrow\ \frac{\sin\alpha+\sin\beta}{\cos\alpha-\cos\beta}=\frac{\text{a}}{\text{b}}$
$\Rightarrow\ \frac{2\sin\big(\frac{\alpha+\beta}{2}\big)\cos\big(\frac{\alpha-\beta}{2}\big)}{-2\sin\big(\frac{\alpha+\beta}{2}\big)\sin\big(\frac{\alpha-\beta}{2}\big)}=\frac{\text{a}}{\text{b}}$ $\Big[\because\ \sin\text{A}+\sin\text{B}=2\sin\Big(\frac{\text{A+B}}{2}\Big)\cos\Big(\frac{\text{A}-\text{B}}{2}\Big)\text{ and }\cos\text{A}+\cos\text{B}$
$\Rightarrow\ \frac{\sin\Big(\frac{\alpha+\beta}{2}\Big)\cos\Big(\frac{\alpha-\beta}{2}\Big)}{-\sin\Big(\frac{\alpha+\beta}{2}\Big)\cos\Big(\frac{\alpha-\beta}{2}\Big)}=\frac{\text{a}}{\text{b}}$
$\Rightarrow\ \cot\Big(\frac{\alpha-\beta}{2}\Big)=-\frac{\text{a}}{\text{b}}$
$\Rightarrow\ \frac{1}{\cot\Big(\frac{\alpha-\beta}{2}\Big)}=\frac{1}{-\frac{\text{a}}{\text{b}}}$
$\Rightarrow\ \tan\Big(\frac{\alpha-\beta}{2}\Big)=-\frac{\text{b}}{\text{a}}$

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 "MCQ" from TRIGONOMETRIC FUNCTIONS→TRIGONOMETRIC FUNCTIONS — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Two dice are thrown:
P is the event that the sum of the scores on the uppermost faces is a multiple of 6.
Q is the event that the sum of the scores on the uppermost faces is at least 10.
R is the event that same scores on both dice. Which of the following pairs is mutually exclusive?
→
Out of $800$ boys in a school, $224$ played cricket, $240$ played hockey and $336$ played basketball. Of the total, $64$ played both basketball and hockey; $80$ played cricket and basketball and $40$ played cricket and hockey; $24$ played all the three games. The number of boys who did not play any game is
→
If the area of the triangle formed by the positive $x-$axis, the normal and the tangent to the circle $(x-2)^{2}+(y-3)^{2}=25$ at the point $(5,7)$ is $A$ then $24 A$ is equal to ...... .
→
If $\frac{3+i \sin \theta}{4-i \cos \theta}, \theta \in[0,2 \pi],$ is a real number, then an argument of $\sin \theta+\mathrm{i} \cos \theta$ is
→
The locus of the centers of the circles such that the point $(2 , 3)$ is the mid point of the chord $5x + 2y = 16$ is :
→
The number of permutations of n different things taking r at a time when 3 particular things are to be included is:
→
What is the length of foot of perpendicular drawn from the point P(3, 4, 5) on y-axis:
→
If the roots of the equation $a{x^2} + bx + c = 0$be $\alpha $and $\beta $, then the roots of the equation $c{x^2} + bx + a = 0$ are
→
Equations of a common tangent to the two hyperbolas $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}}$ $= 1 $ $\&$  $\frac{{{y^2}}}{{{a^2}}} - \frac{{{x^2}}}{{{b^2}}}$ $= 1 $ is :
→
Choose the correct answer. The length of the latus rectum of the ellipse $3\text{x}^2+\text{y}^2=12$ is:
 
→