Advertisements
Advertisements
Question
Solve the following equation:
Advertisements
Solution
\[2 \cos^2 x - 5 \cos x + 2 = 0\]
\[ \Rightarrow 2 \cos^2 x - 4 \cos x - \cos x + 2 = 0\]
\[ \Rightarrow 2 \cos x ( \cos x - 2) - 1 ( \cos x - 2) = 0\]
\[ \Rightarrow (\cos x - 2) ( 2 \cos\theta - 1) = 0\]
\[\therefore 2 \cos x - 1 = 0 \]
\[ \Rightarrow \cos x = \frac{1}{2} \]
\[ \Rightarrow \cos x = \cos \frac{\pi}{3} \]
\[ \Rightarrow x = 2n\pi \pm \frac{\pi}{3}, n \in Z\]
APPEARS IN
RELATED QUESTIONS
If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x
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:
\[\frac{\cos (2\pi + x) cosec (2\pi + x) \tan (\pi/2 + x)}{\sec(\pi/2 + x)\cos x \cot(\pi + x)} = 1\]
Prove that
Prove that:
\[\sin^2 \frac{\pi}{18} + \sin^2 \frac{\pi}{9} + \sin^2 \frac{7\pi}{18} + \sin^2 \frac{4\pi}{9} = 2\]
Prove that:
\[\sec\left( \frac{3\pi}{2} - x \right)\sec\left( x - \frac{5\pi}{2} \right) + \tan\left( \frac{5\pi}{2} + x \right)\tan\left( x - \frac{3\pi}{2} \right) = - 1 .\]
Find x from the following equations:
\[cosec\left( \frac{\pi}{2} + \theta \right) + x \cos \theta \cot\left( \frac{\pi}{2} + \theta \right) = \sin\left( \frac{\pi}{2} + \theta \right)\]
Prove that:
\[\sin \frac{13\pi}{3}\sin\frac{2\pi}{3} + \cos\frac{4\pi}{3}\sin\frac{13\pi}{6} = \frac{1}{2}\]
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then x2 + y2 + z2 is independent of
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
If A lies in second quadrant 3tan A + 4 = 0, then the value of 2cot A − 5cosA + sin A is equal to
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
\[\sin^2 x - \cos x = \frac{1}{4}\]
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[\sin x + \cos x = \sqrt{2}\]
Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]
If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.
Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].
Write the set of values of a for which the equation
Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]
and cos 2x are in A.P.
The number of solution in [0, π/2] of the equation \[\cos 3x \tan 5x = \sin 7x\] is
The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]
General solution of \[\tan 5 x = \cot 2 x\] is
The solution of the equation \[\cos^2 x + \sin x + 1 = 0\] lies in the interval
Find the principal solution and general solution of the following:
sin θ = `-1/sqrt(2)`
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
Solve the following equations:
sin 5x − sin x = cos 3
Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ
Solve the following equations:
sin θ + cos θ = `sqrt(2)`
Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
