Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
sinθ = `1/2`.
Advertisements
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.
संबंधित प्रश्न
Find the principal solution of the following equation :
cot θ = `sqrt(3)`
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 θ = - 1
Find the general solution of the following equation:
sin 2θ = `1/2`
Find the general solution of the following equation:
tan `(2θ)/(3) = sqrt3`
Find the general solution of the following equation:
cot 4θ = – 1
Find the general solution of the following equation:
4 cos2 θ = 3
Find the general solution of the following equation:
cos 4θ = cos 2θ
State whether the following equation has a solution or not?
2sinθ = 3
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)`.
Select the correct option from the given alternatives:
If cos pθ = cos qθ, p ≠ q, then ______.
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 ______.
Select the correct option from the given alternatives:
In ΔABC, ac cos B - bc cos A = _______
If in a triangle, the angles are in A.P. and b: c = `sqrt3: sqrt2`, then A is equal to
If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______.
Select the correct option from the given alternatives:
If tan-1(2x) + tan-1(3x) = `pi/4`, then x = _____
The principal value branch of sec-1x is ______.
Find the principal solutions of the following equation:
sin 2θ = `-1/2`
Find the principal solutions of the following equation:
cot θ = 0
Find the general solutions of the following equation:
sin θ - cos θ = 1
If tan-12x + tan-13x = `pi/4`, then find the value of x.
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
Prove the following:
`cos^-1 "x" = tan^-1 (sqrt(1 - "x"^2)/"x")`, if x > 0
Find the principal solutions of tan x = `-sqrt(3)`
`int (sin (log x))^2/x` log x dx = ?
The general solution of sin 2x = cos 2x is ______
The general solution of the equation tan θ tan 2θ = 1 is given by ______
Which of the following is true in a triangle ABC?
If sin θ + cos θ = 1, then the general value of θ is ______.
If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.
The general solution of 4sin2 x = 1 is ______.
The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval `[pi/2, (3pi)/2]` is ______.
The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ 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 `2sin^-1 3/7` = cos–1β, then find the value of β.
If `sin^-1 4/5 + cos^-1 12/13` = sin–1α, then find the value of α.
