मराठी

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

Advertisements
Advertisements

प्रश्न

Find the general solution of the following equation:

\[\cos 3x = \frac{1}{2}\]
बेरीज
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
  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 2.02 | पृष्ठ २१

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the general solution of the equation cos 4 x = cos 2 x


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


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


Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0


Prove that

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

 


Prove that

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

 


Prove that:
\[\sec\left( \frac{3\pi}{2} - x \right)\sec\left( x - \frac{5\pi}{2} \right) + \tan\left( \frac{5\pi}{2} + x \right)\tan\left( x - \frac{3\pi}{2} \right) = - 1 .\]


If tan x = \[x - \frac{1}{4x}\], then sec x − tan 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 tan x + sec x = \[\sqrt{3}\], 0 < x < π, then x is equal to


sin6 A + cos6 A + 3 sin2 A cos2 A =


If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]

 

\[\sec^2 x = \frac{4xy}{(x + y )^2}\] is true if and only if

 


If sec x + tan x = k, cos x =


Which of the following is correct?


Find the general solution of the following equation:

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

Find the general solution of the following equation:

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

Find the general solution of the following equation:

\[\sin x = \tan x\]

Find the general solution of the following equation:

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

Solve the following equation:

\[\cos 4 x = \cos 2 x\]

Solve the following equation:

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

Solve the following equation:

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

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


The smallest value of x satisfying the equation

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

If \[\tan px - \tan qx = 0\], then the values of θ form a series in

 


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
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]


The smallest positive angle which satisfies the equation ​

\[2 \sin^2 x + \sqrt{3} \cos x + 1 = 0\] is

Find the principal solution and general solution of the following:
sin θ = `-1/sqrt(2)`


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


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


Solve the following equations:
2 cos2θ + 3 sin θ – 3 = θ


Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ


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


Solve the following equations:
cot θ + cosec θ = `sqrt(3)`


Solve the following equations:
cos 2θ = `(sqrt(5) + 1)/4`


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


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×