Solve for x tan-1(1-x1+x)=12tan-1x,x>0 - Mathematics

Question

Solve for x $\tan^{- 1} (\frac{1 - x}{1 + x}) = \frac{1}{2} \tan^{- 1} x, x > 0$

Sum

Solution

From given equation

We have $2 \tan^{- 1} (\frac{1 - x}{1 + x}) = \tan^{- 1} x$

⇒ $2 [\tan^{- 1} 1 - \tan^{- 1} x] = \tan^{- 1} x$

⇒ $2 (\frac{π}{4}) = 3 \tan^{- 1} x$

⇒ $\frac{π}{6} = \tan^{- 1} x$

⇒ x = $\frac{1}{\sqrt{3}}$

shaalaa.com

Inverse Trigonometric Functions

Is there an error in this question or solution?

Q 17 Q 16 Q 18

Chapter 2: Inverse Trigonometric Functions - Solved Examples [Page 26]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12

Chapter 2 Inverse Trigonometric Functions
Solved Examples | Q 17 | Page 26

Video TutorialsVIEW ALL [3]

view
Video Tutorials For All Subjects
Inverse Trigonometric Functions

video tutorial00:04:24
Inverse Trigonometric Functions

video tutorial00:40:14
Inverse Trigonometric Functions

video tutorial00:24:25

RELATED QUESTIONS

Find the domain of the following function:

$f (x) \sin^{- 1} \sqrt{x^{2} - 1}$

Evaluate the following:

$\cot^{- 1} {2 \cos (\sin^{- 1} \frac{\sqrt{3}}{2})}$

In ΔABC, if a = 18, b = 24, c = 30 then find the values of A(ΔABC)

Find the principal value of the following: $\sin^{- 1} (\frac{1}{2})$

Find the principal value of the following: tan^-1(– 1)

Evaluate the following:

$\tan^{- 1} \sqrt{3} - \sec^{- 1} (- 2)$

Evaluate the following:

${cosec}^{- 1} (- \sqrt{2}) + \cot^{- 1} (\sqrt{3})$

If tan⁻¹x + tan⁻¹y + tan⁻¹z = π, then show that $\frac{1}{x y} + \frac{1}{y z} + \frac{1}{z x}$ = 1

Show that $\tan^{- 1} (\frac{1}{2}) + \tan^{- 1} (\frac{2}{11}) = \tan^{- 1} (\frac{3}{4})$

sin[3 sin^-1 (0.4)] = ______.

The principal value of $\tan^{- 1 (\sqrt{3})}$ is ______

The value of $\sin^{- 1} (\cos \frac{53 π}{5})$ is ______

The value of $\sin^{- 1} [\cos (\frac{π}{3})] + \sin^{- 1} [\tan (\frac{5 π}{4})]$ is ______.

Show that $\sin^{- 1} \frac{5}{13} + \cos^{- 1} \frac{3}{5} = \tan^{- 1} \frac{63}{16}$

If tan^-1 3 + tan^-1 x = tan^-1 8, then x = ____________.

${cos}^{- 1} \frac{1}{2} + 2 {sin}^{- 1} \frac{1}{2}$ is equal to ____________.

${sin}^{- 1} (1 - x) - 2 {sin}^{- 1} x = \frac{π}{2}$

The value of ${cos}^{- 1} (cos (\frac{33 π}{5}))$ is ____________.

sin 6θ + sin 4θ + sin 2θ = 0, then θ =

The inverse of $f (x) = \sqrt{3 x^{2} - 4 x + 5}$ is

If $\frac{- 1}{\sqrt{2}} \leq x \leq \frac{1}{\sqrt{2}}$ then $\sin^{- 1} (2 x \sqrt{1 - x^{2}})$ is equal to

Domain and Rariges of cos^–1 is:-

$\sin (\tan^{- 1} x), | x | < 1$ is equal to

If f'(x) = x^–1, then find f(x)

Number of values of x satisfying the system of equations $\sin^{- 1} \sqrt{2 + e^{- 2 x} - 2 e^{- x}} + \sec^{- 1} \sqrt{1 - x^{2} + x^{4}} = \frac{π}{2}$ and $5^{1 + \tan^{- 1} x}$ = 4 + [cos^–1x] is ______ (where [.] denotes greatest integer function)

The value of cos (2cos^–1 x + sin^–1 x) at x = $\frac{1}{5}$ is ______.

Find the value of $\cos (\frac{x}{2})$ , if tan x = $\frac{5}{12}$ and x lies in third quadrant.

If sin^–1x – cos^–1x = $\frac{π}{6}$ , then x = ______.

The value of $\tan (\cos^{- 1} \frac{4}{5} + \tan^{- 1} \frac{2}{3})$ is ______.

Solve for x tan-1(1-x1+x)=12tan-1x,x>0 - Mathematics

Advertisements

Advertisements

Question

Solution

APPEARS IN

Video TutorialsVIEW ALL [3]

RELATED QUESTIONS

Select a course

Solve for x tan-1(1-x1+x)=12tan-1x,x>0 - Mathematics

Advertisements

Advertisements

Question

SolutionShow Solution

APPEARS IN

Video TutorialsVIEW ALL [3]

RELATED QUESTIONS

Select a course

Solution