मराठी

Find the general solution of the following equation: sin x = 1 2

Advertisements
Advertisements

प्रश्न

Find the general solution of the following equation:

\[\sin x = \frac{1}{2}\]
बेरीज
Advertisements

उत्तर

We have:
\[\sin x = \frac{1}{2}\]
The value of x satisfying \[\sin x = \frac{1}{2}\] is \[\frac{\pi}{6}\]

∴ \[\sin x = \frac{1}{2}\]
⇒ \[\sin x = \sin\frac{\pi}{6}\]
⇒ \[x = n\pi + ( - 1 )^n \frac{\pi}{6}\]
\[n \in Z\]
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 11: Trigonometric equations - Exercise 11.1 [पृष्ठ २१]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 11 Trigonometric equations
Exercise 11.1 | Q 1.1 | पृष्ठ २१

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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


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


Prove the:
\[ \sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}} = - \frac{2}{\cos x},\text{ where }\frac{\pi}{2} < x < \pi\]


If \[T_n = \sin^n x + \cos^n x\], prove that \[\frac{T_3 - T_5}{T_1} = \frac{T_5 - T_7}{T_3}\]

 


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


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

Prove that

\[\left\{ 1 + \cot x - \sec\left( \frac{\pi}{2} + x \right) \right\}\left\{ 1 + \cot x + \sec\left( \frac{\pi}{2} + x \right) \right\} = 2\cot x\]

 


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 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


sin6 A + cos6 A + 3 sin2 A cos2 A =


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


If sec x + tan x = k, cos x =


The value of \[\tan1^\circ \tan2^\circ \tan3^\circ . . . \tan89^\circ\] is

 

Find the general solution of the following equation:

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

Find the general solution of the following equation:

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

Solve the following equation:

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

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:

\[\cos x \cos 2x \cos 3x = \frac{1}{4}\]

Solve the following equation:

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

Solve the following equation:

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

Solve the following equation:
\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]


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

 


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


General solution of \[\tan 5 x = \cot 2 x\] is


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


Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`


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

cos 2x = 1 − 3 sin x


Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1


Solve the following equations:
2cos 2x – 7 cos x + 3 = 0


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


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


Find the general solution of the equation 5cos2θ + 7sin2θ – 6 = 0


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×