Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
Advertisements
उत्तर
We have:
⇒ \[\sin9x - \sin x = 0\]
⇒ \[2 \sin \left( \frac{9x - x}{2} \right) \cos \left( \frac{9x + x}{2} \right) = 0\]
⇒ \[\sin \frac{8x}{2} = 0\] or \[\cos \frac{10x}{2} = 0\]
⇒ \[\sin 4x = 0\] or \[\cos 5x = 0\]
⇒ \[4x = n\pi\]
\[n \in Z\] or \[5x = (2n + 1)\frac{\pi}{2}\],
\[n \in Z\]
⇒ \[x = \frac{n\pi}{4}\],
\[n \in Z\] or \[x = (2n + 1)\frac{\pi}{10}\],
APPEARS IN
संबंधित प्रश्न
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 \[T_n = \sin^n x + \cos^n x\], prove that \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]
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:
In a ∆A, B, C, D be the angles of a cyclic quadrilateral, taken in order, prove that cos(180° − A) + cos (180° + B) + cos (180° + C) − sin (90° + D) = 0
Prove that:
\[\tan 4\pi - \cos\frac{3\pi}{2} - \sin\frac{5\pi}{6}\cos\frac{2\pi}{3} = \frac{1}{4}\]
Prove that:
\[\sin\frac{13\pi}{3}\sin\frac{8\pi}{3} + \cos\frac{2\pi}{3}\sin\frac{5\pi}{6} = \frac{1}{2}\]
If tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to
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 x sin 45° cos2 60° = \[\frac{\tan^2 60^\circ cosec30^\circ}{\sec45^\circ \cot^{2^\circ} 30^\circ}\], then x =
If tan θ + sec θ =ex, then cos θ equals
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:
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:
Solve the following equation:
\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]
Solve the following equation:
sin x tan x – 1 = tan x – sin x
Solve the following equation:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0
The smallest value of x satisfying the equation
If a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).
The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]
If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are
Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0
Choose the correct alternative:
`(cos 6x + 6 cos 4x + 15cos x + 10)/(cos 5x + 5cs 3x + 10 cos x)` is equal to
Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.
Find the general solution of the equation 5cos2θ + 7sin2θ – 6 = 0
