If 2 =3 then ( - )= - Vidyadip

MCQ

If $2\tan\alpha=3\tan\beta$ then $\tan(\alpha-\beta)=$

✓
$\frac{\sin2\beta}{5-\cos2\beta}$
B
$\frac{\cos2\beta}{5-\cos2\beta}$
C
$\frac{\sin2\beta}{5+\cos2\beta}$
D
None of these

✓

Answer

Correct option: A.

$\frac{\sin2\beta}{5-\cos2\beta}$

Given:
$2\tan\alpha=3\tan\beta$
Now,
$\tan(\alpha+\beta)=\frac{\tan\alpha-\tan\beta}{1+\tan\alpha\tan\beta}$
$=\frac{\frac{3}{2}\tan\beta-\tan\beta}{1+\Big(\frac{3}{2}\tan\beta\Big)\tan\beta}$
$=\frac{3\tan\beta-2\tan\beta}{2+3\tan^2\beta}$
$=\frac{\tan\beta}{2+3\tan^2\beta}$
$=\frac{\frac{\sin\beta}{\cos\beta}}{2+3\frac{\sin^2\beta}{\cos^2\beta}}$
$=\frac{\sin\beta\cos\beta}{2\cos\beta+3\sin\beta}$
$=\frac{\sin\beta\cos\beta}{2+\sin^2\beta}$
$=\frac{2\sin\beta\cos\beta}{4+2-\cos2\beta}$
$=\frac{\sin2\beta}{4+1-cos2\beta}$
$\therefore\tan(\alpha+\beta)=\frac{\sin2\beta}{5-\cos2\beta}$

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 "MCQ" from Trigonometric Ratios Of Compounds→Trigonometric Ratios Of Compounds — 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 values of $\theta $ in $[0, 2\pi]$ satisfying the equation $2{\sin ^2}\theta = 4 + 3$$\cos \theta $ are

How many numbers lying between $500$ and $600$ can be formed with the help of the digits $1, \,2, \,3, \,4, \,5,\, 6$ when the digits are not to be repeated

If the normals at two points $P$ and $Q$ of a parabola ${y^2} = 4ax$ intersect at a third point $R$ on the curve, then the product of ordinates of $P$ and $Q$ is

Mean deviation is least if it is taken about :-

How many numbers can be made with the digits $3, 4, 5, 6, 7, 8$ lying between $3000$ and $4000$ which are divisible by $5$ while repetition of any digit is not allowed in any number

$\lim\limits_{x \rightarrow 2} \frac{3^{x}+3^{3-x}-12}{3^{-x / 2}-3^{1-x}}$ is equal to

The average age of two brothers is 9 years It is increased by 9 years when their mothers age is also included then the age of mother is:

If area of quadrilateral formed by tangents drawn at ends of latus rectum of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is equal to square of distance between centre and one focus of hyperbola, then $e^3$ is ($e$ is eccentricity of hyperbola)

The value of $0.\mathop {234}\limits^{\,\,\, \bullet \,\, \bullet } $ is

The probabilities of three mutually exclusive events A, B and C are given by $\frac{2}{3}$, $\frac{1}{4}$ and $\frac{1}{6}$respectively. The statement