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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

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

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प्रश्न

Select the correct option from the given alternatives:

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

पर्याय

  • `pi/6, (7pi)/6`

  • `pi/6, (5pi)/6`

  • `pi/6, (8pi)/6`

  • `(7pi)/6, pi/3`

MCQ
रिकाम्या जागा भरा
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उत्तर

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

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Trigonometric Functions - Miscellaneous exercise 3 [पृष्ठ १०६]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 3 Trigonometric Functions
Miscellaneous exercise 3 | Q 1.02 | पृष्ठ १०६

संबंधित प्रश्‍न

Find the principal solution of the following equation :

cot θ = `sqrt(3)`


Find the principal solution of the following equation:

cot θ = 0


Find the principal solution of the following equation:

sin θ = `-1/2`


Find the principal solution of the following equation:

`sqrt(3)` cosecθ + 2 = 0 


Find the general solution of the following equation:

cot θ = 0.


Find the general solution of the following equation:

sec θ = `sqrt(2)`.


Find the general solution of the following equation:

tan θ = - 1


Find the general solution of the following equation:

sin 2θ = `1/2`


Find the general solution of the following equation:

cot 4θ = – 1


Find the general solution of the following equation: 

tan3θ = 3 tanθ.


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


In ΔABC, prove that `sin(("B" − "C")/2) = (("b" − "c")/"a")cos  "A"/(2)`.


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


With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c2 .


Select the correct option from the given alternatives:

The principal solutions of equation sin θ = `- 1/2` are ______.


Select the correct option from the given alternatives:

In Δ ABC if ∠A = 45°, ∠B = 30°, then the ratio of its sides are


The principal value branch of sec-1x is ______.


Find the principal solutions of the following equation:

tan 3θ = - 1


Find the principal solutions of the following equation:

cot θ = 0


Find the general solutions of the following equation:

`tan theta = - sqrt3`


Find the general solutions of the following equation:

`tan^2 theta = 3`


Find the general solutions of the following equation:

sin2 θ - cos2 θ = 1


With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`


If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.


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`


If `tan^-1 "x" + tan^-1 "y" + tan^-1 "z" = pi/2,` then show that xy + yz + zx = 1


Find the principal solutions of cos 2𝑥 = 1


If sin-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos-1 x is _______.


`cos^-1 (cos  (4pi)/3)` = ______.


`int 1/(sin x * cos x)` dx = ?


If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?


The general solution of sec θ = `sqrt2` is


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


If f(x) = sin-1`(sqrt((1 - x)/2))`, then f'(x) = ?


The principal solutions of cot x = `sqrt3` are ______.


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


The number of solutions of `sin^2 theta = 1/2` in [0, π] is ______.


The value of `tan^-1  1/3 + tan^-1  1/5 + tan^-1  1/7 + tan^-1  1/8` is ______.


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


Which of the following is true in a triangle ABC?


The general value of θ in the equation `2sqrt(3) cos theta = tan theta` is ______.


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


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


The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.


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


The general solution to cos100x – sin100x = 1 is ______.


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


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