Advertisements
Advertisements
प्रश्न
Solve the following equation:
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 `tan x = sqrt3`
Find the principal and general solutions of the equation sec x = 2
Find the general solution of the equation cos 4 x = cos 2 x
Find the general solution of the equation sin x + sin 3x + sin 5x = 0
If \[\tan x = \frac{b}{a}\] , then find the values of \[\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}}\].
If \[\cot x \left( 1 + \sin x \right) = 4 m \text{ and }\cot x \left( 1 - \sin x \right) = 4 n,\] \[\left( m^2 + n^2 \right)^2 = mn\]
Prove the:
\[ \sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}} = - \frac{2}{\cos x},\text{ where }\frac{\pi}{2} < x < \pi\]
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:
\[\frac{\cos (2\pi + x) cosec (2\pi + x) \tan (\pi/2 + x)}{\sec(\pi/2 + x)\cos x \cot(\pi + x)} = 1\]
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
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 \[\frac{3\pi}{4} < \alpha < \pi, \text{ then }\sqrt{2\cot \alpha + \frac{1}{\sin^2 \alpha}}\] is equal to
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
If x is an acute angle and \[\tan x = \frac{1}{\sqrt{7}}\], then the value of \[\frac{{cosec}^2 x - \sec^2 x}{{cosec}^2 x + \sec^2 x}\] is
If tan θ + sec θ =ex, then cos θ equals
If sec x + tan x = k, cos x =
The value of \[\tan1^\circ \tan2^\circ \tan3^\circ . . . \tan89^\circ\] is
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:
Solve the following equation:
Solve the following equation:
\[\cot x + \tan x = 2\]
Solve the following equation:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]
If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
In (0, π), the number of solutions of the equation \[\tan x + \tan 2x + \tan 3x = \tan x \tan 2x \tan 3x\] is
General solution of \[\tan 5 x = \cot 2 x\] is
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 θ + sin 3θ + sin 5θ = 0
Solve the following equations:
sin θ + cos θ = `sqrt(2)`
Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`
Choose the correct alternative:
If tan 40° = λ, then `(tan 140^circ - tan 130^circ)/(1 + tan 140^circ * tan 130^circ)` =
Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
