Advertisements
Advertisements
Question
Solve the following equations:
2cos 2x – 7 cos x + 3 = 0
Advertisements
Solution
2 cos2x – 7 cos x + 3 = 0
2 cos2x – 6 cos x – cos x + 3 = 0
2 cos x (cos x – 3) – 1(cos x – 3) = 0
(2 cos x – 1)(cos x – 3) = 0
2 cos x – 1 = 0 or cos x – 3 = 0
cos x = `1/2` or cos x = 3|
Since – 1 ≤ cos x ≤ 1, we have
cos x = 3 is not possible.
∴ cos x = `1/2`
cos x = `cos pi/3`
The general solution is x = `2"n"pi +- pi/3`, n ∈ Z
APPEARS IN
RELATED QUESTIONS
Find the principal and general solutions of the equation `tan x = sqrt3`
Find the general solution of the equation sin x + sin 3x + sin 5x = 0
If \[cosec x - \sin x = a^3 , \sec x - \cos x = b^3\], then prove that \[a^2 b^2 \left( a^2 + b^2 \right) = 1\]
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 \[m^2 \leq 2\]
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
If \[\frac{3\pi}{4} < \alpha < \pi, \text{ then }\sqrt{2\cot \alpha + \frac{1}{\sin^2 \alpha}}\] is equal to
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 =
Which of the following is incorrect?
The value of \[\tan1^\circ \tan2^\circ \tan3^\circ . . . \tan89^\circ\] is
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
sin x tan x – 1 = tan x – sin x
Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].
Write the number of points of intersection of the curves
Choose the correct alternative:
If cos pθ + cos qθ = 0 and if p ≠ q, then θ is equal to (n is any integer)
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.
