मराठी

Find the General Solution of the Following Equation: Sin 9 X = Sin X - Mathematics

Advertisements
Advertisements

प्रश्न

Find the general solution of the following equation:

\[\sin 9x = \sin x\]
बेरीज
Advertisements

उत्तर

We have:

\[\sin9x = \sin x\]

⇒ \[\sin9x - \sin x = 0\]

⇒ \[2 \sin \left( \frac{9x - x}{2} \right) \cos \left( \frac{9x + x}{2} \right) = 0\]

⇒ \[\sin \frac{8x}{2} = 0\] 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 \[x = (2n + 1)\frac{\pi}{10}\],

\[n \in Z\]
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 11: Trigonometric equations - Exercise 11.1 [पृष्ठ २१]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 11 Trigonometric equations
Exercise 11.1 | Q 2.03 | पृष्ठ २१

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the general solution of the equation cos 3x + cos x – cos 2x = 0


If \[T_n = \sin^n x + \cos^n x\], prove that \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]


Prove that:

\[3\sin\frac{\pi}{6}\sec\frac{\pi}{3} - 4\sin\frac{5\pi}{6}\cot\frac{\pi}{4} = 1\]

 


In a ∆ABC, prove that:

\[\tan\frac{A + B}{2} = \cot\frac{C}{2}\]

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:
\[\sin \frac{13\pi}{3}\sin\frac{2\pi}{3} + \cos\frac{4\pi}{3}\sin\frac{13\pi}{6} = \frac{1}{2}\]


If tan x + sec x = \[\sqrt{3}\], 0 < x < π, then x is equal to


\[\sec^2 x = \frac{4xy}{(x + y )^2}\] is true if and only if

 


The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is


The value of \[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\] is

 

The value of \[\tan1^\circ \tan2^\circ \tan3^\circ . . . \tan89^\circ\] is

 

Find the general solution of the following equation:

\[\tan x = - \frac{1}{\sqrt{3}}\]

Find the general solution of the following equation:

\[\sin 2x = \cos 3x\]

Find the general solution of the following equation:

\[\tan x + \cot 2x = 0\]

Find the general solution of the following equation:

\[\tan 3x = \cot x\]

Find the general solution of the following equation:

\[\tan 2x \tan x = 1\]

Find the general solution of the following equation:

\[\sin 2x + \cos x = 0\]

Solve the following equation:
\[\sin^2 x - \cos x = \frac{1}{4}\]


Solve the following equation:

\[2 \cos^2 x - 5 \cos x + 2 = 0\]

Solve the following equation:

\[\cos x \cos 2x \cos 3x = \frac{1}{4}\]

Solve the following equation:

\[\cos x + \sin x = \cos 2x + \sin 2x\]

Solve the following equation:

\[\sqrt{3} \cos x + \sin x = 1\]


Solve the following equation:

`cosec  x = 1 + cot x`


Solve the following equation:
\[\cot x + \tan x = 2\]

 


Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2


Solve the following equation:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]


If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.


Write the set of values of a for which the equation

\[\sqrt{3} \sin x - \cos x = a\] has no solution.

If \[\tan px - \tan qx = 0\], then the values of θ form a series in

 


The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is


Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°

2 cos2x + 1 = – 3 cos x


Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°

cos 2x = 1 − 3 sin x


Solve the following equations:
sin θ + cos θ = `sqrt(2)`


Choose the correct alternative:
If cos pθ + cos qθ = 0 and if p ≠ q, then θ is equal to (n is any integer)


Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval


Solve the equation sin θ + sin 3θ + sin 5θ = 0


Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×