If A=2 B+ B, then 2 (A-B) is equal to - Vidyadip

MCQ

If $\tan A=2 \tan B+\cot B$, then $2 \tan (A-B)$ is equal to

A
tan B
B
2 tan B
✓
cot B
D
2 cot B

✓

Answer

Correct option: C.

cot B

(C)
$2 \tan (A-B)=2\left(\frac{\tan A-\tan B}{1+\tan A \tan B}\right)$
$=2\left[\frac{2 \tan B+\cot B-\tan B}{1+(2 \tan B+\cot B) \tan B}\right]$
$\ldots[\because \tan A=2 \tan B+\cot B]$
$=2\left[\frac{\tan B+\cot B}{2\left(1+\tan ^2 B\right)}\right]$
$=\frac{\cot B \left(\tan ^2 B+1\right)}{1+\tan ^2 B}=\cot B$

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

Slope of a line which cuts intercepts of equal lengths on the axes is

Which of the following function is not continuous at $x=0$ ?

If $f (x)=\left\{\begin{array}{cc}\frac{x^6-\frac{1}{64}}{x^3-\frac{1}{8}}, & x \neq \frac{1}{2} \\ k , & x=\frac{1}{2}\end{array}\right.$ is continuous at $x=\frac{1}{2}$, then the value of k is

If $z + z ^{-1}=1$, then $z ^{100}+ z ^{-100}$ is equal to

A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set $S=\{1,2,3,4,5,6,7\}$ and reports that it is even. The probability that it is actually even is

The length of the latus-rectum of the parabola whose focus is $\left(\frac{ u ^2}{2 g} \sin 2 \alpha,-\frac{ u ^2}{2 g} \cos 2 \alpha\right)$ and directrix is $y=\frac{ u ^2}{2 g}$, is

Equation of locus of a point, so that the segment joining the points (3, 2) and (-5, 1) subtends a right angle at that point, is

If the function $f(x)=\left\{\begin{aligned}(\cos x)^{\frac{1}{x}} & ; x \neq 0 \\ k & ; x=0\end{aligned}\right.$ is continuous at $x=0$, then the value of k is

The number of permutations of $n$ different things taking $r$ at a time when $3$ particular things are to be included is :

A circle $x^2+y^2+2 g x+2 f y+ c =0$ passing through (4, -2) is concentric to the circle $x^2+y^2-2 x+4 y+20=0$ then the value of c will be