English

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

Advertisements
Advertisements

Question

Find the general solution of the following equation:

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

Solution

We have:
\[\cos x = - \frac{\sqrt{3}}{2}\]
The value of x satisfying 

\[\cos x = - \frac{\sqrt{3}}{2}\] is \[\frac{7\pi}{6}\]
⇒ \[\cos x = \cos\frac{7\pi}{6}\]
⇒ \[x = 2n\pi \pm \frac{7\pi}{6}\]
\[n \in Z\]
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 1.2 | Page 21

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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 \[\tan x = \frac{a}{b},\] show that

\[\frac{a \sin x - b \cos x}{a \sin x + b \cos x} = \frac{a^2 - b^2}{a^2 + b^2}\]

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 \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]


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 ∆ABC, prove that:

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

 


Find x from the following equations:
\[cosec\left( \frac{\pi}{2} + \theta \right) + x \cos \theta \cot\left( \frac{\pi}{2} + \theta \right) = \sin\left( \frac{\pi}{2} + \theta \right)\]


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 sec \[x = x + \frac{1}{4x}\], then sec x + tan x = 

 

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

 


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

 


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

 


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


Which of the following is correct?


Find the general solution of the following equation:

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

Find the general solution of the following equation:

\[\tan 2x \tan x = 1\]

Solve the following equation:

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

Solve the following equation:

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

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:
\[\sin x + \cos x = \sqrt{2}\]


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


Solve the following equation:
3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0


Solve the following equation:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]


If \[2 \sin^2 x = 3\cos x\]. where \[0 \leq x \leq 2\pi\], then find the value of x.


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


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 


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°

sin4x = sin2x


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


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:
`(cos 6x + 6 cos 4x + 15cos x + 10)/(cos 5x + 5cs 3x + 10 cos x)` is equal to


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


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


Find the general solution of the equation sinx – 3sin2x + sin3x = cosx – 3cos2x + cos3x


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×