Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
उत्तर
We have:
⇒ \[\sin2x = \sin \frac{\pi}{3}\]
⇒ \[2x = n\pi + ( - 1 )^n \frac{\pi}{3}\]
⇒ \[x = \frac{n\pi}{2} + ( - 1 )^n \frac{\pi}{6}\],
APPEARS IN
संबंधित प्रश्न
Find the principal and general solutions of the equation `tan x = sqrt3`
Find the general solution of the equation cos 3x + cos x – cos 2x = 0
If \[x = \frac{2 \sin x}{1 + \cos x + \sin x}\], then prove that
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: \[\tan\frac{11\pi}{3} - 2\sin\frac{4\pi}{6} - \frac{3}{4} {cosec}^2 \frac{\pi}{4} + 4 \cos^2 \frac{17\pi}{6} = \frac{3 - 4\sqrt{3}}{2}\]
Prove that:
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 \[\frac{\pi}{2} < x < \pi, \text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}}\] is equal to
The value of \[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\] 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:
\[\sqrt{3} \cos x + \sin x = 1\]
Solve the following equation:
If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.
Write the number of points of intersection of the curves
Write the solution set of the equation
Write the number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].
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
The number of solution in [0, π/2] of the equation \[\cos 3x \tan 5x = \sin 7x\] is
A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] 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 cos2x + 1 = – 3 cos x
Solve the following equations:
2 cos2θ + 3 sin θ – 3 = θ
Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ
Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1
Solve the equation sin θ + sin 3θ + sin 5θ = 0
If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation ______.
Find the general solution of the equation 5cos2θ + 7sin2θ – 6 = 0
Find the general solution of the equation sinx – 3sin2x + sin3x = cosx – 3cos2x + cos3x