हिंदी

Find the General Solution of the Following Equation: Cos 3 X = 1 2 - Mathematics

Advertisements
Advertisements

प्रश्न

Find the general solution of the following equation:

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

उत्तर

We have:

\[\cos3x = \frac{1}{2}\]

⇒ \[\cos3x = \cos \frac{\pi}{3}\]

⇒ \[3x = 2n\pi \pm \frac{\pi}{3}\]

\[n \in Z\]

⇒ \[x = \frac{2n\pi}{3} \pm \frac{\pi}{9}\]

\[n \in Z\]
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 11: Trigonometric equations - Exercise 11.1 [पृष्ठ २१]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 11 Trigonometric equations
Exercise 11.1 | Q 2.02 | पृष्ठ २१

वीडियो ट्यूटोरियलVIEW ALL [1]

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


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

 

In a ∆ABC, prove that:

\[\cos\left( \frac{A + B}{2} \right) = \sin\frac{C}{2}\]

 


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


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


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


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


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


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


Find the general solution of the following equation:

\[cosec x = - \sqrt{2}\]

Find the general solution of the following equation:

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

Find the general solution of the following equation:

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

Solve the following equation:

\[\tan^2 x + \left( 1 - \sqrt{3} \right) \tan x - \sqrt{3} = 0\]

Solve the following equation:

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

Solve the following equation:
 cosx + sin x = cos 2x + sin 2x

 


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


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


Write the number of points of intersection of the curves

\[2y = 1\] and \[y = \cos x, 0 \leq x \leq 2\pi\].
 

In (0, π), the number of solutions of the equation ​ \[\tan x + \tan 2x + \tan 3x = \tan x \tan 2x \tan 3x\] is 


If \[\sqrt{3} \cos x + \sin x = \sqrt{2}\] , then general value of x is


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


The number of values of x in the interval [0, 5 π] satisfying the equation \[3 \sin^2 x - 7 \sin x + 2 = 0\] is


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

cos 2x = 1 − 3 sin x


Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ


Choose the correct alternative:
If tan α and tan β are the roots of x2 + ax + b = 0 then `(sin(alpha + beta))/(sin alpha sin beta)` is equal to


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


Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.


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


If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×