English

Find the General Solution of the Following Equation: Tan X = − 1 √ 3

Advertisements
Advertisements

Question

Find the general solution of the following equation:

\[\tan x = - \frac{1}{\sqrt{3}}\]
Sum
Advertisements

Solution

We have:

\[\tan x = - \frac{1}{\sqrt{3}}\]
The value of x satisfying \[\tan x = - \frac{1}{\sqrt{3}}\] is \[- \frac{\pi}{6}\].

∴ \[\tan x = - \frac{1}{\sqrt{3}}\]

⇒ \[\tan x = \tan ( - \frac{\pi}{6})\]

⇒ \[x = n\pi - \frac{\pi}{6}\],

\[n \in Z\]
shaalaa.com
  Is there an error in this question or solution?
Chapter 11: Trigonometric equations - Exercise 11.1 [Page 21]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 11 Trigonometric equations
Exercise 11.1 | Q 1.5 | Page 21

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the general solution of cosec x = –2


Find the general solution of the equation cos 4 x = cos 2 x


If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x


If \[\cot x \left( 1 + \sin x \right) = 4 m \text{ and }\cot x \left( 1 - \sin x \right) = 4 n,\] \[\left( m^2 + n^2 \right)^2 = mn\]


Prove the:
\[ \sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}} = - \frac{2}{\cos x},\text{ where }\frac{\pi}{2} < x < \pi\]


If \[T_n = \sin^n x + \cos^n x\], prove that  \[2 T_6 - 3 T_4 + 1 = 0\]


Prove that

\[\frac{cosec(90^\circ + x) + \cot(450^\circ + x)}{cosec(90^\circ - x) + \tan(180^\circ - x)} + \frac{\tan(180^\circ + x) + \sec(180^\circ - x)}{\tan(360^\circ + x) - \sec( - x)} = 2\]

 


Prove that:

\[\tan\frac{5\pi}{4}\cot\frac{9\pi}{4} + \tan\frac{17\pi}{4}\cot\frac{15\pi}{4} = 0\]

 


If \[\frac{3\pi}{4} < \alpha < \pi, \text{ then }\sqrt{2\cot \alpha + \frac{1}{\sin^2 \alpha}}\] is equal to


If \[cosec x + \cot x = \frac{11}{2}\], then tan x =

 


If tan θ + sec θ =ex, then cos θ equals


The value of \[\tan1^\circ \tan2^\circ \tan3^\circ . . . \tan89^\circ\] is

 

Find the general solution of the following equation:

\[\cos x = - \frac{\sqrt{3}}{2}\]

Find the general solution of the following equation:

\[\sin 9x = \sin x\]

Solve the following equation:

\[\tan^2 x + \left( 1 - \sqrt{3} \right) \tan x - \sqrt{3} = 0\]

Solve the following equation:

\[\cos 4 x = \cos 2 x\]

Solve the following equation:

\[\sin x + \sin 5x = \sin 3x\]

Solve the following equation:

\[\cos x + \sin x = \cos 2x + \sin 2x\]

Solve the following equation:

\[\sin x + \sin 2x + \sin 3x + \sin 4x = 0\]

Solve the following equation:

\[\sin 3x - \sin x = 4 \cos^2 x - 2\]

Solve the following equation:

\[\tan x + \tan 2x = \tan 3x\]

Solve the following equation:

\[\tan 3x + \tan x = 2\tan 2x\]

Solve the following equation:
\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]


Solve the following equation:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0


Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2


Solve the following equation:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]


If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.


Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].


The smallest value of x satisfying the equation

\[\sqrt{3} \left( \cot x + \tan x \right) = 4\] is 

If \[\cot x - \tan x = \sec x\], then, x is equal to

 


If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =


If \[\sqrt{3} \cos x + \sin x = \sqrt{2}\] , then general value of x is


Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`


Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`


Solve the following equations:
sin 5x − sin x = cos 3


Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ


Find the general solution of the equation sinx – 3sin2x + sin3x = cosx – 3cos2x + cos3x


The minimum value of 3cosx + 4sinx + 8 is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×