Advertisements
Advertisements
Question
Select the correct option from the given alternatives:
The principal solutions of equation sin θ = `- 1/2` are ______.
Options
`(5pi)/6, pi/6`
`(7pi)/6, (11pi)/6`
`pi/6, (7pi)/6`
`(7pi)/6, pi/3`
Advertisements
Solution
The principal solutions of equation sin θ = `- 1/2` are `bb(underline((7pi)/6, (11pi)/6)`.
RELATED QUESTIONS
Find the principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
Find the general solution of the following equation:
cos 4θ = cos 2θ
Find the general solution of the following equation:
tan3θ = 3 tanθ.
Find the general solution of the following equation:
cosθ + sinθ = 1.
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 has a solution or not?
2sinθ = 3
In ΔABC, prove that `sin(("B" − "C")/2) = (("b" − "c")/"a")cos "A"/(2)`.
With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c2 .
Select the correct option from the given alternatives:
If cos pθ = cos qθ, p ≠ q, then ______.
`"cos"^-1 ("cos" (7pi)/6)` = _________.
Select the correct option from the given alternatives:
The value of cot (tan-12x + cot-12x) is
If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______.
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:
sin θ - cos θ = 1
In ΔABC, prove that `("a - b")^2 cos^2 "C"/2 + ("a + b")^2 sin^2 "C"/2 = "c"^2`
In Δ ABC, if cos A = sin B - cos C then show that it is a right-angled triangle.
If 2 tan-1(cos x) = tan-1(2 cosec x), then find the value of x.
Prove the following:
`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 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 sin x − 1 = 0
Find the principal solutions of tan x = `-sqrt(3)`
The value of tan 57°- tan 12°- tan 57° tan 12° is ______.
If 2 cos2 θ + 3 cos θ = 2, then permissible value of cos θ is ________.
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
Which of the following equations has no solution?
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 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 ______.
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 ______.
General solution of the equation sin 2x – sin 4x + sin 6x = 0 is ______.
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.
The general solution of cot 4x = –1 is ______.
If `2sin^-1 3/7` = cos–1β, then find the value of β.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
