हिंदी

Find the general solution of the following equation: sinθ = 12. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Find the general solution of the following equation:

sinθ = `1/2`.

योग

उत्तर

The general solution of sin θ = sin α is 
θ = nπ + (– 1)nα, n ∈ Z

Now,
`sinθ = 1/2 = sin  π/6     ...[∵ sin  pi/(6) = 1/2]`

∴ the required general solution is θ = nπ + (– 1)n `π/6`, n ∈ Z.

shaalaa.com
Trigonometric Equations and Their Solutions
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Trigonometric Functions - Exercise 3.1 [पृष्ठ ७५]

संबंधित प्रश्न

Find the principal solution of the following equation:

cot θ = 0


Find the general solution of the following equation :

cosθ = `sqrt(3)/(2)`


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 `(2θ)/(3) = sqrt3`.


Find the general solution of the following equation:

4cos2θ  = 3.


Find the general solution of the following equation: 

tan3θ = 3 tanθ.


State whether the following equation have solution or not?

cos 2θ = – 1


State whether the following equation has a solution or not?

cos2θ = – 1.


State whether the following equation have solution or not?

3 tanθ = 5


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


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:

The general solution of sec x = `sqrt(2)` is ______.


Select the correct option from the given alternatives:

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


`"cos"["tan"^-1 1/3 + "tan"^-1 1/2]` = ______


If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is ______.


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:

sin θ - cos θ = 1


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


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


State whether the following equation has a solution or not?

3 sin θ = 5


Show that `2 cot^(-1)  3/2 +  sec^(-1)  13/12 = π/2`


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


The general solution of sec θ = `sqrt2` is


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


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


The number of solutions of cos 2θ = sin θ in (0, 2π) is ______


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 ______ 


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 number of solutions of sin x + sin 3x + sin 5x = 0 in the interval `[pi/2, (3pi)/2]` is ______.


Find the principal solutions of cot θ = 0


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


General solution of the equation sin 2x – sin 4x + sin 6x = 0 is ______.


Which of the following equation has no solution?


The number of principal solutions of tan 2θ = 1 is ______.


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


Find the general solution of sin θ + sin 3θ + sin 5θ = 0


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×