Advertisements
Advertisements
प्रश्न
Solve the following equation:
Advertisements
उत्तर
\[ \Rightarrow 2 - 2 \cos^2 x + \sqrt{3} \cos x + 1 = 0\]
\[ \Rightarrow 2 \cos^2 x - \sqrt{3} \cos x - 3 = 0\]
\[ \Rightarrow 2 \cos^2 x - 2\sqrt{3} \cos x + \sqrt{3} \cos x - 3 = 0\]
\[ \Rightarrow 2 \cos x (\cos x - \sqrt{3}) + \sqrt{3} (\cos x - \sqrt{3}) = 0\]
\[ \Rightarrow (2 \cos x + \sqrt{3}) (\cos x - \sqrt{3}) = 0\]
⇒ \[(2 \cos x + \sqrt{3}) = 0\] 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
संबंधित प्रश्न
Find the principal and general solutions of the equation `cot x = -sqrt3`
Find the general solution of cosec x = –2
If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x
If \[\tan x = \frac{b}{a}\] , then find the values of \[\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}}\].
If \[\tan x = \frac{a}{b},\] show that
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:
\[\frac{\cos (2\pi + x) cosec (2\pi + x) \tan (\pi/2 + x)}{\sec(\pi/2 + x)\cos x \cot(\pi + x)} = 1\]
Prove that
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
In a ∆ABC, prove that:
If tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to
If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to
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
If \[\frac{3\pi}{4} < \alpha < \pi, \text{ then }\sqrt{2\cot \alpha + \frac{1}{\sin^2 \alpha}}\] is equal to
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:
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
\[\sqrt{3} \cos x + \sin x = 1\]
Solve the following equation:
`cosec x = 1 + cot 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 solutions of the equation
\[4 \sin x - 3 \cos x = 7\]
Write the number of points of intersection of the curves
If \[2 \sin^2 x = 3\cos x\]. where \[0 \leq x \leq 2\pi\], then find the value of x.
If a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
If \[\cot x - \tan x = \sec x\], then, x is equal to
In (0, π), the number of solutions of the equation \[\tan x + \tan 2x + \tan 3x = \tan x \tan 2x \tan 3x\] is
The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.
Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 sin2x + 1 = 3 sin x
Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ
Solve the equation sin θ + sin 3θ + sin 5θ = 0
If a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2
In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.
