If 2 A=3 B, then 2 B 5- 2 B is equal to - Vidyadip

MCQ

If $2 \tan A=3 \tan B$, then $\frac{\sin 2 B}{5-\cos 2 B}$ is equal to

A
$\tan A-\tan B$
✓
$\tan (A-B)$
C
$\tan (A+B)$
D
$\tan (A+2 B)$

✓

Answer

Correct option: B.

$\tan (A-B)$

(B)
$2 \tan A=3 \tan B$
$\Rightarrow \tan A =\frac{3}{2} \tan B=\frac{3}{2} t \quad[$ Let $\tan B =t]$
$\sin 2 B=\frac{2 t }{1+ t ^2}, \cos 2 B=\frac{1- t ^2}{1+ t ^2}$
$\therefore \frac{\sin 2 B}{5-\cos 2 B}=\frac{\left(\frac{2 t}{1+t^2}\right)}{5-\left(\frac{1-t^2}{1+t^2}\right)}=\frac{2 t}{4+6 t^2}$
$=\frac{t}{2+3 t^2}=\frac{\frac{3 t}{2}-t}{1+\frac{3 t^2}{2}}$
$=\tan ( A - B )$

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 Trigonometry – II→Trigonometry – II — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Let f: R → R be defined as $f(x)=\frac{x^2-x+4}{x^2+x+4}$
Then the range of the function $f (x)$ is

The equation of the hyperbola with vertices ( $0, \pm 15$ ) and foci $(0, \pm 20)$ is

If $\frac{3+i \sin \theta}{4-i \cos \theta}, \theta \in[0,2 \pi]$, is a real number, then an argument of $\sin \theta+ i \cos \theta$ is

The real values of $x$ and $y$ for which the equation $(x+i y)(2-3 i)=4+i$ is satisfied, are

If $\cos2\text{x}+2\cos\text{x}=1$ then, $(2-\cos^2\text{x})\sin^2\text{x}$ is equal to :

If $f : R \rightarrow R$ be a mapping defined by $f ( x )=x^3+5$, then $f ^{-1}(x)$ is equal to

If $\left(\frac{1+ i }{1- i }\right)^{ m }=1$, then the least positive integral value of $m$ is

Let $a, b, c, d, e$ be the observations with mean m and standard deviation $s$. The standard deviation of the observations $a + k, b + k, c + k, d + k, e + k$ is:

Let $\alpha$ be the distance between the line -x + y = 2 and x - y = 2 and \[\beta\] be the distance between the lines $4 x-3 y=5$ and $6 y-8 x=1$, then

One card is drawn from a pack of $52$ cards. The probability that it is the card of a king or spade is :