Advertisements
Advertisements
Question
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
Advertisements
Solution
The principal value of tan θ lies in `(- pi/2, pi/2)`
Since tan θ = `- 1/sqrt(3) > 0`
The principal value of tan θ lies in the IV quadrant.
tan θ = `- 1/sqrt(3)`
= `- tan pi/6`
tan θ = `tan ( - pi/6)`
θ = `- pi/6` is the principal solution.
The general solution of tan θ is
θ = `"n"pi - pi/6`, n ∈ Z
APPEARS IN
RELATED QUESTIONS
Find the general solution of the equation cos 3x + cos x – cos 2x = 0
If \[\tan x = \frac{a}{b},\] show that
If \[T_n = \sin^n x + \cos^n x\], prove that \[\frac{T_3 - T_5}{T_1} = \frac{T_5 - T_7}{T_3}\]
Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
Prove that:
If \[0 < x < \frac{\pi}{2}\], and if \[\frac{y + 1}{1 - y} = \sqrt{\frac{1 + \sin x}{1 - \sin x}}\], then y is equal to
If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then
The value of \[\tan1^\circ \tan2^\circ \tan3^\circ . . . \tan89^\circ\] is
Find the general solution of the following equation:
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
Write the number of solutions of the equation
\[4 \sin x - 3 \cos x = 7\]
The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]
In (0, π), the number of solutions of the equation \[\tan x + \tan 2x + \tan 3x = \tan x \tan 2x \tan 3x\] is
The solution of the equation \[\cos^2 x + \sin x + 1 = 0\] lies in the interval
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
