Advertisements
Advertisements
प्रश्न
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the principal and general solutions of the equation sec x = 2
If \[\sin x + \cos x = m\], then prove that \[\sin^6 x + \cos^6 x = \frac{4 - 3 \left( m^2 - 1 \right)^2}{4}\], where \[m^2 \leq 2\]
Prove that: tan 225° cot 405° + tan 765° cot 675° = 0
Prove that:
\[\sin^2 \frac{\pi}{18} + \sin^2 \frac{\pi}{9} + \sin^2 \frac{7\pi}{18} + \sin^2 \frac{4\pi}{9} = 2\]
Prove that:
\[\tan 4\pi - \cos\frac{3\pi}{2} - \sin\frac{5\pi}{6}\cos\frac{2\pi}{3} = \frac{1}{4}\]
If A lies in second quadrant 3tan A + 4 = 0, then the value of 2cot A − 5cosA + sin A is equal to
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
If sec x + tan x = k, cos x =
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
`cosec x = 1 + cot x`
Write the general solutions of tan2 2x = 1.
If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.
Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]
and cos 2x are in A.P.
Write the number of points of intersection of the curves
In (0, π), the number of solutions of the equation \[\tan x + \tan 2x + \tan 3x = \tan x \tan 2x \tan 3x\] is
The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.
The solution of the equation \[\cos^2 x + \sin x + 1 = 0\] lies in the interval
Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval
Choose the correct alternative:
If sin α + cos α = b, then sin 2α is equal to
