English

Find the Principal and General Solutions of the Equation `Tan X = Sqrt3`

Advertisements
Advertisements

Question

Find the principal and general solutions of the equation `tan x = sqrt3`

Advertisements

Solution

shaalaa.com
  Is there an error in this question or solution?

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the principal and general solutions of the equation sec x = 2


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


Find the general solution of the equation cos 3x + cos x – cos 2x = 0


If \[\tan x = \frac{b}{a}\] , then find the values of \[\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}}\].


If \[cosec x - \sin x = a^3 , \sec x - \cos x = b^3\], then prove that \[a^2 b^2 \left( a^2 + b^2 \right) = 1\]


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


If \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that  \[ab + a - b + 1 = 0\]


Prove that:
\[\sin^2 \frac{\pi}{18} + \sin^2 \frac{\pi}{9} + \sin^2 \frac{7\pi}{18} + \sin^2 \frac{4\pi}{9} = 2\]

 

If sec \[x = x + \frac{1}{4x}\], then sec x + tan x = 

 

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


\[\sec^2 x = \frac{4xy}{(x + y )^2}\] is true if and only if

 


If x is an acute angle and \[\tan x = \frac{1}{\sqrt{7}}\], then the value of \[\frac{{cosec}^2 x - \sec^2 x}{{cosec}^2 x + \sec^2 x}\] is


If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then


Find the general solution of the following equation:

\[\tan 2x \tan x = 1\]

Find the general solution of the following equation:

\[\tan mx + \cot nx = 0\]

Find the general solution of the following equation:

\[\sin x = \tan x\]

Solve the following equation:

\[2 \cos^2 x - 5 \cos x + 2 = 0\]

Solve the following equation:

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

Solve the following equation:

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

Solve the following equation:

\[\tan x + \tan 2x + \tan 3x = 0\]

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


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


Write the number of solutions of the equation
\[4 \sin x - 3 \cos x = 7\]


Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]

 and cos 2x are in A.P.


The smallest value of x satisfying the equation

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

The smallest positive angle which satisfies the equation ​

\[2 \sin^2 x + \sqrt{3} \cos x + 1 = 0\] is

In (0, π), the number of solutions of the equation ​ \[\tan x + \tan 2x + \tan 3x = \tan x \tan 2x \tan 3x\] is 


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


The solution of the equation \[\cos^2 x + \sin x + 1 = 0\] lies in the interval


Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°

2 cos2x + 1 = – 3 cos x


Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°

cos 2x = 1 − 3 sin x


Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0


Choose the correct alternative:
If sin α + cos α = b, then sin 2α is equal to


Solve the equation sin θ + sin 3θ + sin 5θ = 0


Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`


If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation ______.


In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×