Advertisements
Advertisements
Question
Find the general solution of the following equation:
Solution
We have:
∴ \[\tan x = - \frac{1}{\sqrt{3}}\]
⇒ \[\tan x = \tan ( - \frac{\pi}{6})\]
⇒ \[x = n\pi - \frac{\pi}{6}\],
APPEARS IN
RELATED QUESTIONS
Find the principal and general solutions of the equation sec x = 2
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 \[\sin x + \cos x = m\], then prove that \[\sin^6 x + \cos^6 x = \frac{4 - 3 \left( m^2 - 1 \right)^2}{4}\], where \[m^2 \leq 2\]
If \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that \[ab + a - b + 1 = 0\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[\frac{T_3 - T_5}{T_1} = \frac{T_5 - T_7}{T_3}\]
Prove that: tan 225° cot 405° + tan 765° cot 675° = 0
Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]
Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0
Prove that
Prove that
Prove that:
If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to
sin6 A + cos6 A + 3 sin2 A cos2 A =
If x sin 45° cos2 60° = \[\frac{\tan^2 60^\circ cosec30^\circ}{\sec45^\circ \cot^{2^\circ} 30^\circ}\], then x =
Find the general solution of the following equation:
Find the general solution of the following equation:
Find the general solution of the following equation:
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:
Solve the following equation:
Solve the following equation:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0
If \[2 \sin^2 x = 3\cos x\]. where \[0 \leq x \leq 2\pi\], then find the value of x.
The smallest value of x satisfying the equation
If \[\cos x + \sqrt{3} \sin x = 2,\text{ then }x =\]
If \[\cot x - \tan x = \sec x\], then, x is equal to
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
If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are
Solve the following equations:
2 cos2θ + 3 sin θ – 3 = θ
Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1
Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`
Solve the equation sin θ + sin 3θ + sin 5θ = 0
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.
Find the general solution of the equation 5cos2θ + 7sin2θ – 6 = 0
