मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Select the correct option from the given alternatives: The principal solutions of equation sin θ = -12 are ______.

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प्रश्न

Select the correct option from the given alternatives:

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

पर्याय

  • `(5pi)/6, pi/6`

  • `(7pi)/6, (11pi)/6`

  • `pi/6, (7pi)/6`

  • `(7pi)/6, pi/3`

MCQ
रिकाम्या जागा भरा
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उत्तर

The principal solutions of equation sin θ = `- 1/2`  are `bb(underline((7pi)/6, (11pi)/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 1.01 | 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:

`sqrt(3)` cosecθ + 2 = 0 


Find the general solution of the following equation:

cosec θ = - √2.


Find the general solution of the following equation:

4sin2θ = 1.


Find the general solution of the following equation:

sin θ = tan θ


State whether the following equation has a solution or not?

2sinθ = 3


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.


Select the correct option from the given alternatives:

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


Select the correct option from the given alternatives:

If polar coordinates of a point are `(2, pi/4)`, then its cartesian coordinates are


If `sqrt3 cos x − sin x = 1`, then general value of x is ______.


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


If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______.


Select the correct option from the given alternatives:

`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____


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


Find the general solutions of the following equation:

sin θ - cos θ = 1


In Δ ABC, prove that `cos(("A" - "B")/2) = (("a" + "b")/"c")sin  "C"/2` .


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


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.


Show that `cos^-1  sqrt3/2 + 2 sin^-1  sqrt3/2 = (5pi)/6`.


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 | < 1, then prove that

`2 tan^-1 "x" = tan^-1 ("2x"/(1 - "x"^2)) = sin^-1 ("2x"/(1 + "x"^2)) = cos^-1 ((1 - "x"^2)/(1 + "x"^2))`


The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______


Find the principal solutions of cosec x = 2


Find the principal solutions of sin x − 1 = 0


The value of tan 57°- tan 12°- tan 57° tan 12° is ______.


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


`[sin (tan^-1  3/4)]^2 + [sin(tan^-1  4/3)]^2 = ?`


If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?


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


Which of the following equations has no solution?


If function

f(x) = `x - |x|/x, x < 0`
      = `x + |x|/x, x > 0`
      = 1, x = 0, then


The value of sin 18° is ______.


The value of θ in (π, 2π) satisfying the equation sin2θ - cos2θ = 1 is ______ 


The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 is ______ 


The general solution of sin 2x = cos 2x is ______ 


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


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


Find the principal solutions of cot θ = 0


The general solution of x(1 + y2)1/2 dx + y(1 + x2)1/2 dy = 0 is ______.


If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.


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


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