English

Find the General Solution of the Following Equation: Sin 2 X = √ 3 2

Advertisements
Advertisements

Question

Find the general solution of the following equation:

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

Solution

We have:

\[\sin2x = \frac{\sqrt{3}}{2}\]

⇒ \[\sin2x = \sin \frac{\pi}{3}\]

⇒ \[2x = n\pi + ( - 1 )^n \frac{\pi}{3}\]

\[n \in Z\]

⇒ \[x = \frac{n\pi}{2} + ( - 1 )^n \frac{\pi}{6}\],

\[n \in Z\]
shaalaa.com
  Is there an error in this question or solution?
Chapter 11: Trigonometric equations - Exercise 11.1 [Page 21]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 11 Trigonometric equations
Exercise 11.1 | Q 2.01 | Page 21

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the general solution of the equation  sin x + sin 3x + sin 5x = 0


If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x


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 \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that  \[ab + a - b + 1 = 0\]


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


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 cos 570° sin 510° + sin (−330°) cos (−390°) = 0

Prove that

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

 


In a ∆ABC, prove that:

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

 


Prove that:

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

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


If \[\frac{3\pi}{4} < \alpha < \pi, \text{ then }\sqrt{2\cot \alpha + \frac{1}{\sin^2 \alpha}}\] is equal to


If \[cosec x + \cot x = \frac{11}{2}\], then tan x =

 


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


If \[cosec x + \cot x = \frac{11}{2}\], then tan x =

 


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

 

Find the general solution of the following equation:

\[\cos x = - \frac{\sqrt{3}}{2}\]

Find the general solution of the following equation:

\[\sqrt{3} \sec x = 2\]

Find the general solution of the following equation:

\[\tan mx + \cot nx = 0\]

Solve the following equation:

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

Solve the following equation:

\[3 \cos^2 x - 2\sqrt{3} \sin x \cos x - 3 \sin^2 x = 0\]

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:

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

Solve the following equation:

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

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

 


Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]


Solve the following equation:
\[\sin x - 3\sin2x + \sin3x = \cos x - 3\cos2x + \cos3x\]


Write the solution set of the equation 

\[\left( 2 \cos x + 1 \right) \left( 4 \cos x + 5 \right) = 0\] in the interval [0, 2π].

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

 


A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] is

 

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


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


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


In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×