मराठी

Solve the Following Equation: Sin X + Sin 2 X + Sin 3 = 0

Advertisements
Advertisements

प्रश्न

Solve the following equation:

\[\sin x + \sin 2x + \sin 3 = 0\]
बेरीज
Advertisements

उत्तर

\[\sin x + \sin 2x + \sin 3 = 0\]
\[\Rightarrow \sin x + \sin3x + \sin2x = 0\]
\[ \Rightarrow 2 \sin \left( \frac{4x}{2} \right) \cos \left( \frac{2x}{2} \right) + \sin2x = 0\]
\[ \Rightarrow 2 \sin2x\cos x + \sin2x = 0\]
\[ \Rightarrow \sin2x (2 \cos x + 1) = 0\]

\[\Rightarrow \sin2x = 0\] or
\[2 \cos x + 1 = 0\]
\[\Rightarrow \sin2x = \sin 0\] or
\[\cos x = - \frac{1}{2} \Rightarrow \cos x = \cos \frac{2\pi}{3}\]
⇒ \[x = \frac{n\pi}{2}, n \in Z\] or
\[x = 2m\pi \pm \frac{2\pi}{3}\],
\[m \in Z\]
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 11: Trigonometric equations - Exercise 11.1 [पृष्ठ २२]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 11 Trigonometric equations
Exercise 11.1 | Q 4.6 | पृष्ठ २२

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the principal and general solutions of the equation sec x = 2


If \[\sin x + \cos x = m\], then prove that \[\sin^6 x + \cos^6 x = \frac{4 - 3 \left( m^2 - 1 \right)^2}{4}\], where \[m^2 \leq 2\]


Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]


Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0


Prove that

\[\frac{cosec(90^\circ + x) + \cot(450^\circ + x)}{cosec(90^\circ - x) + \tan(180^\circ - x)} + \frac{\tan(180^\circ + x) + \sec(180^\circ - x)}{\tan(360^\circ + x) - \sec( - x)} = 2\]

 


Prove that

\[\frac{\sin(180^\circ + x) \cos(90^\circ + x) \tan(270^\circ - x) \cot(360^\circ - x)}{\sin(360^\circ - x) \cos(360^\circ + x) cosec( - x) \sin(270^\circ + x)} = 1\]

 


Prove that:
\[\sin^2 \frac{\pi}{18} + \sin^2 \frac{\pi}{9} + \sin^2 \frac{7\pi}{18} + \sin^2 \frac{4\pi}{9} = 2\]

 

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


sin2 π/18 + sin2 π/9 + sin2 7π/18 + sin2 4π/9 =


Which of the following is incorrect?


Find the general solution of the following equation:

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

Find the general solution of the following equation:

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

Find the general solution of the following equation:

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

Find the general solution of the following equation:

\[\sin x = \tan x\]

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


Solve the following equation:

\[\sin x + \sin 5x = \sin 3x\]

Solve the following equation:

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

Solve the following equation:

\[\sin 3x - \sin x = 4 \cos^2 x - 2\]

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


Solve the following equation:

\[\sin x + \cos x = 1\]

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


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


If \[\cos x + \sqrt{3} \sin x = 2,\text{ then }x =\]

 


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


A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval


The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]


If \[4 \sin^2 x = 1\], then the values of x are

 


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 solution of the equation \[\cos^2 x + \sin x + 1 = 0\] lies in the interval


Find the principal solution and general solution of the following:
tan θ = `- 1/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:
`sin theta + sqrt(3) cos theta` = 1


If a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2 


Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×