हिंदी

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

Advertisements
Advertisements

प्रश्न

Find the general solution of the following equation:

\[\sin x = \frac{1}{2}\]
योग
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
  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 1.1 | पृष्ठ २१

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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


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


If \[x = \frac{2 \sin x}{1 + \cos x + \sin x}\], then prove that

\[\frac{1 - \cos x + \sin x}{1 + \sin x}\] is also equal to a.

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:

\[3\sin\frac{\pi}{6}\sec\frac{\pi}{3} - 4\sin\frac{5\pi}{6}\cot\frac{\pi}{4} = 1\]

 


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


Prove that:

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

If \[0 < x < \frac{\pi}{2}\], and if \[\frac{y + 1}{1 - y} = \sqrt{\frac{1 + \sin x}{1 - \sin x}}\], then y is equal to


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


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

 


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


If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then


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

 

Find the general solution of the following equation:

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

Find the general solution of the following equation:

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

Find the general solution of the following equation:

\[\sin x = \tan x\]

Solve the following equation:

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

Solve the following equation:
\[\cot x + \tan x = 2\]

 


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


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


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

 


Write the number of points of intersection of the curves

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

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


The smallest value of x satisfying the equation

\[\sqrt{3} \left( \cot x + \tan x \right) = 4\] is 

If a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).


The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]


Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`


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 5x − sin x = cos 3


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


Solve the following equations:
sin θ + cos θ = `sqrt(2)`


Choose the correct alternative:
If tan 40° = λ, then `(tan 140^circ - tan 130^circ)/(1 + tan 140^circ *  tan 130^circ)` =


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


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


If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×