The value of ( 3 -x ) ( 3 +x ) is: - Vidyadip

MCQ

The value of $\tan\text{x}\tan\Big(\frac{\pi}{3}-\text{x}\Big)\tan\Big(\frac{\pi}{3}+\text{x}\Big)$ is:

A
$\cot3\text{x}$
B
$2\cot3\text{x}$
✓
$\tan3\text{x}$
D
$3\tan3\text{x}$

✓

Answer

Correct option: C.

$\tan3\text{x}$

$\frac{\pi}{3}=60^\circ$
$\tan\text{x}\tan(60^\circ-\text{x})\tan(60^\circ+\text{x})\\=\tan\text{x}\times\frac{\tan60^\circ-\tan\text{x}}{1+\tan60^\circ\tan\text{x}}\times\frac{\tan60^\circ+\tan\text{x}}{1-\tan60^\circ\tan\text{x}}$
$=\tan\text{x}\times\frac{\sqrt{3}-\tan\text{x}}{1+\sqrt{3\tan\text{x}}}\times\frac{\sqrt{3}+\tan\text{x}}{1-\sqrt{3}\tan\text{x}}$
$=\frac{\tan\text{x}(3-\tan^2\text{x})}{1-3\tan^2\text{x}}$
$=\frac{3\tan\text{x}-\tan^3\text{x}}{1-3\tan^2\text{x}}$
$=\tan3\text{x}$

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

There are $5$ volumes of Mathematics among $25$ books. They are arranged on a shelf in random order. The probability that the volumes of Mathematics stand in increasing order from left to right (the volumes are not necessarily kept side by side) is

The sixth term of an $A.P.$ is equal to $2$, the value of the common difference of the $A.P.$ which makes the product ${a_1}{a_4}{a_5}$ least is given by

The coefficient of $x^{18}$ in the product $(1+x)(1-x)^{10}\left(1+x+x^2\right)^9$ is?

The term independent of $y$ in the expansion of ${({y^{ - 1/6}} - {y^{1/3}})^9}$ is

If $\text{A}=\sin2\text{x}+\cos4\text{x}, $ then for all real x:

The focal chord to ${y^2} = 16x$ is tangent to ${(x - 6)^2} + {y^2} = 2$, then the possible value of the slope of this chord, are

Two dice are thrown simultaneously. Find the probability of getting an even number as the sum.

If vertices of a parallelogram are respectively $(0, 0)$, $(1, 0)$, $(2, 2)$ and $(1, 2)$, then angle between diagonals is

Let $\bigcup \limits_{i=1}^{50} X_{i}=\bigcup \limits_{i=1}^{n} Y_{i}=T$ where each $X_{i}$ contains $10$ elements and each $Y_{i}$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of sets $X_{i}$ 's and exactly $6$ of sets $Y_{i}$ 's, then $n$ is equal to

Let $S_1,S_2$ and $S_3$ be three circles of unit radius which touch each other externally. The common tangent to each pair of circles are drawn and extended so that they can intersect and form a triangle $ABC$ with circumradius $R,$ then $R$ is equal to