Advertisements
Advertisements
Question
Solve the following equation:
Advertisements
Solution
\[ \Rightarrow 2 - 2 \cos^2 x + \sqrt{3} \cos x + 1 = 0\]
\[ \Rightarrow 2 \cos^2 x - \sqrt{3} \cos x - 3 = 0\]
\[ \Rightarrow 2 \cos^2 x - 2\sqrt{3} \cos x + \sqrt{3} \cos x - 3 = 0\]
\[ \Rightarrow 2 \cos x (\cos x - \sqrt{3}) + \sqrt{3} (\cos x - \sqrt{3}) = 0\]
\[ \Rightarrow (2 \cos x + \sqrt{3}) (\cos x - \sqrt{3}) = 0\]
⇒ \[(2 \cos x + \sqrt{3}) = 0\] or
\[ \Rightarrow \cos x = - \frac{\sqrt{3}}{2} \]
\[ \Rightarrow \cos x = \cos \frac{5\pi}{6} \]
\[ \Rightarrow x = 2n\pi \pm \frac{5\pi}{6}, n \in\]
APPEARS IN
RELATED QUESTIONS
Find the principal and general solutions of the equation `tan x = sqrt3`
Find the general solution of cosec x = –2
Prove that: tan 225° cot 405° + tan 765° cot 675° = 0
Prove that:
Prove that
Prove that:
\[\sin^2 \frac{\pi}{18} + \sin^2 \frac{\pi}{9} + \sin^2 \frac{7\pi}{18} + \sin^2 \frac{4\pi}{9} = 2\]
In a ∆A, B, C, D be the angles of a cyclic quadrilateral, taken in order, prove that cos(180° − A) + cos (180° + B) + cos (180° + C) − sin (90° + D) = 0
Prove that:
\[\tan 4\pi - \cos\frac{3\pi}{2} - \sin\frac{5\pi}{6}\cos\frac{2\pi}{3} = \frac{1}{4}\]
Prove that:
If tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to
If sec \[x = x + \frac{1}{4x}\], then sec x + tan x =
sin2 π/18 + sin2 π/9 + sin2 7π/18 + sin2 4π/9 =
If x sin 45° cos2 60° = \[\frac{\tan^2 60^\circ cosec30^\circ}{\sec45^\circ \cot^{2^\circ} 30^\circ}\], then x =
If tan θ + sec θ =ex, then cos θ equals
If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0
If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.
If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.
If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.
The smallest value of x satisfying the equation
If a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).
The number of solution in [0, π/2] of the equation \[\cos 3x \tan 5x = \sin 7x\] is
If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =
If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 sin2x + 1 = 3 sin x
Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ
Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0
Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ
Solve the following equations:
cot θ + cosec θ = `sqrt(3)`
Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`
Choose the correct alternative:
`(cos 6x + 6 cos 4x + 15cos x + 10)/(cos 5x + 5cs 3x + 10 cos x)` is equal to
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation ______.
If a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2
