मराठी

Solve the following equation: sin x + sin 5 x = sin 3 x - Mathematics

Advertisements
Advertisements

प्रश्न

Solve the following equation:

\[\sin x + \sin 5x = \sin 3x\]
बेरीज

उत्तर

\[\sin x + \sin5x = \sin3x\]
\[\Rightarrow 2 \sin\left( \frac{6x}{2} \right) \cos \left( \frac{4x}{2} \right) = \sin3x\]
\[ \Rightarrow 2 \sin3x \cos2x = \sin3x\]
\[ \Rightarrow 2 \sin3x \cos2x - \sin3x = 0\]
\[ \Rightarrow \sin3x (2 \cos2x - 1) = 0\]
\[\Rightarrow \sin3x = 0\] or
\[(2 \cos2x - 1) = 0\]
\[\Rightarrow \sin3x = \sin 0\] or
\[\cos2x = \frac{1}{2} = \cos \frac{\pi}{3}\]
\[\cos2x = \frac{1}{2} = \cos \frac{\pi}{3}\] or
\[2x = 2m\pi \pm \frac{\pi}{3}\]
⇒ \[x = \frac{n\pi}{3}, n \in Z\] or
\[x = m\pi \pm \frac{\pi}{6}, m \in Z\]
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 11: Trigonometric equations - Exercise 11.1 [पृष्ठ २२]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 11 Trigonometric equations
Exercise 11.1 | Q 4.3 | पृष्ठ २२

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the principal and general solutions of the equation `tan x = sqrt3`


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 \[\tan x = \frac{a}{b},\] show that

\[\frac{a \sin x - b \cos x}{a \sin x + b \cos x} = \frac{a^2 - b^2}{a^2 + b^2}\]

If \[cosec x - \sin x = a^3 , \sec x - \cos x = b^3\], then prove that \[a^2 b^2 \left( a^2 + b^2 \right) = 1\]


If \[\cot x \left( 1 + \sin x \right) = 4 m \text{ and }\cot x \left( 1 - \sin x \right) = 4 n,\] \[\left( m^2 + n^2 \right)^2 = mn\]


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 \[m^2 \leq 2\]


If \[T_n = \sin^n x + \cos^n x\], prove that  \[2 T_6 - 3 T_4 + 1 = 0\]


Prove that:  tan 225° cot 405° + tan 765° cot 675° = 0


Prove that:

\[\sin\frac{8\pi}{3}\cos\frac{23\pi}{6} + \cos\frac{13\pi}{3}\sin\frac{35\pi}{6} = \frac{1}{2}\]

 


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


Find x from the following equations:
\[x \cot\left( \frac{\pi}{2} + \theta \right) + \tan\left( \frac{\pi}{2} + \theta \right)\sin \theta + cosec\left( \frac{\pi}{2} + \theta \right) = 0\]


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


Prove that:

\[\sin\frac{10\pi}{3}\cos\frac{13\pi}{6} + \cos\frac{8\pi}{3}\sin\frac{5\pi}{6} = - 1\]

If sec \[x = x + \frac{1}{4x}\], then sec x + tan x = 

 

If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to

 


If tan \[x = - \frac{1}{\sqrt{5}}\] and θ lies in the IV quadrant, then the value of cos x is

 

If A lies in second quadrant 3tan A + 4 = 0, then the value of 2cot A − 5cosA + sin A is equal to


Which of the following is incorrect?


Which of the following is correct?


Find the general solution of the following equation:

\[\sin 2x = \frac{\sqrt{3}}{2}\]

Solve the following equation:

\[\cos 4 x = \cos 2 x\]

Solve the following equation:

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

Solve the following equation:

\[\sin 2x - \sin 4x + \sin 6x = 0\]

Solve the following equation:

\[\tan x + \tan 2x = \tan 3x\]

Solve the following equation:
4sinx cosx + 2 sin x + 2 cosx + 1 = 0 


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


If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.

 

If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.


The smallest positive angle which satisfies the equation ​

\[2 \sin^2 x + \sqrt{3} \cos x + 1 = 0\] is

If \[\cot x - \tan x = \sec x\], then, x is equal to

 


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 theta + sqrt(3) cos theta` = 1


Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`


Solve the following equations:
cos 2θ = `(sqrt(5) + 1)/4`


Choose the correct alternative:
`(cos 6x + 6 cos 4x + 15cos x + 10)/(cos 5x + 5cs 3x + 10 cos x)` is equal to


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


The minimum value of 3cosx + 4sinx + 8 is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×