Advertisements
Advertisements
प्रश्न
Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`
Advertisements
उत्तर
`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
संबंधित प्रश्न
Find the general solution of the equation cos 3x + cos x – cos 2x = 0
If \[T_n = \sin^n x + \cos^n x\], prove that \[\frac{T_3 - T_5}{T_1} = \frac{T_5 - T_7}{T_3}\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[2 T_6 - 3 T_4 + 1 = 0\]
Prove that: \[\tan\frac{11\pi}{3} - 2\sin\frac{4\pi}{6} - \frac{3}{4} {cosec}^2 \frac{\pi}{4} + 4 \cos^2 \frac{17\pi}{6} = \frac{3 - 4\sqrt{3}}{2}\]
Prove that:
If tan x + sec x = \[\sqrt{3}\], 0 < x < π, then x is equal to
If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]
If sec x + tan x = k, cos x =
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:
Solve the following equation:
Solve the following equation:
Solve the following equation:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0
Write the number of points of intersection of the curves
The number of solution in [0, π/2] of the equation \[\cos 3x \tan 5x = \sin 7x\] is
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
sin4x = sin2x
Solve the following equations:
2 cos2θ + 3 sin θ – 3 = θ
Choose the correct alternative:
If tan α and tan β are the roots of x2 + ax + b = 0 then `(sin(alpha + beta))/(sin alpha sin beta)` is equal to
Find the general solution of the equation 5cos2θ + 7sin2θ – 6 = 0
