हिंदी

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

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

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

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Find the general solution of cosec x = –2


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


Find the general solution for each of the following equations sec2 2x = 1– tan 2x


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


Prove that

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

 


In a ∆ABC, prove that:
cos (A + B) + cos C = 0


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:
\[\sin\frac{13\pi}{3}\sin\frac{8\pi}{3} + \cos\frac{2\pi}{3}\sin\frac{5\pi}{6} = \frac{1}{2}\]


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

 


\[\sqrt{\frac{1 + \cos x}{1 - \cos x}}\] is equal to

 


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 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 correct?


Find the general solution of the following equation:

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

Find the general solution of the following equation:

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

Find the general solution of the following equation:

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

Solve the following equation:

\[4 \sin^2 x - 8 \cos x + 1 = 0\]

Solve the following equation:

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

Solve the following equation:

\[\cos x + \cos 3x - \cos 2x = 0\]

Solve the following equation:

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

Solve the following equation:

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

Solve the following equation:
 sin x tan x – 1 = tan x – sin x

 


Write the number of solutions of the equation
\[4 \sin x - 3 \cos x = 7\]


Write the general solutions of tan2 2x = 1.

 

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

 

Write the number of points of intersection of the curves

\[2y = - 1 \text{ and }y = cosec x\]

Write the number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].


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


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:
cot θ = `sqrt(3)`


Choose the correct alternative:
If sin α + cos α = b, then sin 2α is equal to


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×