English

Select the correct option from the given alternatives: The principal solutions of equation cot θ = 3 are ______. - Mathematics and Statistics

Advertisements
Advertisements

Question

Select the correct option from the given alternatives:

The principal solutions of equation cot θ = `sqrt3` are ______.

Options

  • `pi/6, (7pi)/6`

  • `pi/6, (5pi)/6`

  • `pi/6, (8pi)/6`

  • `(7pi)/6, pi/3`

MCQ
Fill in the Blanks
Advertisements

Solution

The principal solutions of equation cot θ = `sqrt3` are `bb(underline(pi/6, (7pi)/6)`.

shaalaa.com
Trigonometric Equations and Their Solutions
  Is there an error in this question or solution?
Chapter 3: Trigonometric Functions - Miscellaneous exercise 3 [Page 106]

RELATED QUESTIONS

Find the principal solution of the following equation: 

Sec θ = `(2)/sqrt(3)`


Find the principal solution of the following equation:

`sqrt(3)` cosecθ + 2 = 0 


Find the general solution of the following equation:

tan θ = `(1)/(sqrt(3))`


Find the general solution of the following equation:

cosec θ = - √2.


Find the general solution of the following equation:

tan θ = - 1


Find the general solution of the following equation:

cot 4θ = – 1


Find the general solution of the following equation: 

tan3θ = 3 tanθ.


State whether the following equation has a solution or not?

cos2θ = – 1.


In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.


With the usual notations prove that `2{asin^2  "C"/(2) + "c"sin^2  "A"/(2)}` = a – b + c.


In Δ ABC, prove that a3 sin(B – C) + b3sin(C – A) + c3sin(A – B) = 0


In ΔABC, if a cos A = b cos B then prove that the triangle is either a right angled or an isosceles traingle.


Select the correct option from the given alternatives:

In ΔABC, ac cos B - bc cos A = _______


`"cos"^-1 ("cos" (7pi)/6)` = _________.


Select the correct option from the given alternatives:

The value of cot (tan-12x + cot-12x) is


The principal value of sin1 `(- sqrt3/2)` is ______.


Select the correct option from the given alternatives:

`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______


Select the correct option from the given alternatives:

In any ΔABC, if acos B = bcos A, then the triangle is


In Δ ABC, if cos A = sin B - cos C then show that it is a right-angled triangle.


If sin-1(1 - x) - 2 sin-1x =  `pi/2`, then find the value of x.


If tan-12x + tan-13x = `pi/4`, then find the value of x.


Prove the following:

`cos^-1 "x" = tan^-1 (sqrt(1 - "x"^2)/"x")`, if x > 0


Prove the following:

`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0


If x, y, z are positive, then prove that

`tan^-1 (("x - y")/(1 + "xy")) + tan^-1 (("y - z")/(1 + "yz")) + tan^-1 (("z - x")/(1 + "zx")) = 0`


Find the principal solutions of cos 2𝑥 = 1


`cos^-1 (cos  (4pi)/3)` = ______.


`int (sin (log x))^2/x` log x dx = ?


If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is


If x + y = `pi/2`, then the maximum value of sin x. sin y is.


The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.


The value of sin 18° is ______.


If 4 sin-1x + 6 cos-1 x = 3π then x = ______.


The general solution of the equation tan θ tan 2θ = 1 is given by ______ 


Which of the following is true in a triangle ABC?


The general solution of cot θ + tan θ = 2 is ______.


If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.


The general solution of cosec x = `-sqrt2` is ______ 


The equation 3sin2x + 10 cos x – 6 = 0 is satisfied, if ______.


If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.


If y = `(2sinα)/(1 + cosα + sinα)`, then value of `(1 - cos α + sin α)/(1 + sin α)` is ______.


Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.


If a = sin θ + cos θ, b = sin3 θ + cos3 θ, then ______.


Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.


If `sin^-1  4/5 + cos^-1  12/13` = sin–1α, then find the value of α.


If tan θ + sec θ = `sqrt(3)`, find the general value of θ.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×