The value of tan x-tan 3 x whenever defined never lie between

The correct option is A Let y=tan x/tan 3x=tan x/3 tan x tan^3 x/1 3 tan^3 x y=1 3 tan^2 x/3 tan^2 x=1/3 tan^2 x/1 1/3.tan^2 x Hence, y should never lie betwe ...

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Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

The value of ...

Question

The value of $\frac{t a n x}{t a n 3 x}$ whenever defined never lie between

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Solution

The correct option is A

$L e t y = \frac{t a n x}{t a n 3 x} = \frac{t a n x}{\frac{3 t a n x - t a n^{3} x}{1 - 3 t a n^{3} x}} y = \frac{1 - 3 t a n^{2} x}{3 - t a n^{2} x} = \frac{\frac{1}{3} - t a n^{2} x}{1 - \frac{1}{3} . t a n^{2} x}$

Hence, y should never lie between $\frac{1}{3}$ and 3 whenever defined.

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Similar questions

The value of $\frac{t a n x}{t a n 3 x}$ whenever defined never lie between

Q. Show that the value of

\frac{tan x}{tan 3 x}

wherever defined never lies between

\frac{1}{3}

and

3

(a) If x be real prove that the expression

\frac{x + 2}{2 x^{2} + 3 x + 6}

takes all values in the interval

[- {\frac{1}{13}}^{'} \frac{1}{3}]

(b) Show that the value of

\frac{t a n x}{t a n 3 x}

\frac{s i n x c o s 3 x}{c o s x s i n 3 x}

Whenever defined never lies between

1 / 3

and

3

\frac{3 x^{2} + 9 x + 17}{3 x^{2} + 9 x + 7}

Q. The minimum value of the function

f (x) = \frac{sin x}{\sqrt{1 - {cos}^{2} x}} + \frac{cos x}{\sqrt{1 - {sin}^{2} x}} + \frac{tan x}{\sqrt{{sec}^{2} x} - 1} + \frac{cot x}{\sqrt{c o s e c^{2} x} - 1}

whenever it is defined is

The value of $\frac{t a n 3 x - t a n 2 x - t a n x}{t a n 3 x t a n 2 x t a n x}$ is

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The value of tan xtan 3x whenever defined never lie between

The correct option is A Let y=tan xtan 3x=tan x3 tan x−tan3 x1−3 tan3xy=1−3 tan2 x3−tan2 x=13−tan2 x1−13.tan2 x Hence, y should never lie between 13 and 3 whenever defined.

The value of $\frac{t a n x}{t a n 3 x}$ whenever defined never lie between