Advertisements
Advertisements
Question
Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`
Advertisements
Solution
`1/cot theta = 1/sqrt(3)`
⇒ tan θ = `1/sqrt(3)`
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 I quadrant.
tan θ = `1/sqrt(3)`
= `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 principal and general solutions of the equation `cot x = -sqrt3`
If \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that \[ab + a - b + 1 = 0\]
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.
If \[\cos x + \sqrt{3} \sin x = 2,\text{ then }x =\]
The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]
The smallest positive angle which satisfies the equation
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°
cos 2x = 1 − 3 sin x
Solve the following equations:
2 cos2θ + 3 sin θ – 3 = θ
Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval
Choose the correct alternative:
`(cos 6x + 6 cos 4x + 15cos x + 10)/(cos 5x + 5cs 3x + 10 cos x)` is equal to
If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation ______.
