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प्रश्न
Select the correct option from the given alternatives:
The principal solutions of equation sin θ = `- 1/2` are ______.
विकल्प
`(5pi)/6, pi/6`
`(7pi)/6, (11pi)/6`
`pi/6, (7pi)/6`
`(7pi)/6, pi/3`
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उत्तर
The principal solutions of equation sin θ = `- 1/2` are `bb(underline((7pi)/6, (11pi)/6)`.
संबंधित प्रश्न
Find the principal solution of the following equation:
sin θ = `-1/2`
Find the general solution of the following equation:
sinθ = `1/2`.
Find the general solution of the following equation :
cosθ = `sqrt(3)/(2)`
Find the general solution of the following equation:
cosec θ = - √2.
Find the general solution of the following equation:
sin 2θ = `1/2`
Find the general solution of the following equation:
4sin2θ = 1.
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)`.
With the usual notations prove that `2{asin^2 "C"/(2) + "c"sin^2 "A"/(2)}` = a – b + c.
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:
In Δ ABC if ∠A = 45°, ∠B = 30°, then the ratio of its sides are
Select the correct option from the given alternatives:
In ΔABC if c2 + a2 – b2 = ac, then ∠B = ____.
The principal value of sin–1 `(- sqrt3/2)` is ______.
Select the correct option from the given alternatives:
`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______
The principal value branch of sec-1x is ______.
Select the correct option from the given alternatives:
In any ΔABC, if acos B = bcos A, then the triangle is
Find the general solutions of the following equation:
sin θ - cos 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 sin-1(1 - x) - 2 sin-1x = `pi/2`, then find the value of x.
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
Show that `tan^-1 1/2 = 1/3 tan^-1 11/2`
Show that `cos^-1 sqrt3/2 + 2 sin^-1 sqrt3/2 = (5pi)/6`.
Show that `2 cot^(-1) 3/2 + sec^(-1) 13/12 = π/2`
Prove the following:
`cos^-1 "x" = tan^-1 (sqrt(1 - "x"^2)/"x")`, if x > 0
The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______
Find the principal solutions of cosec x = 2
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
`[sin (tan^-1 3/4)]^2 + [sin(tan^-1 4/3)]^2 = ?`
The value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` is ______.
The number of solutions of cos 2θ = sin θ in (0, 2π) is ______
The value of sin 18° is ______.
The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 is ______
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 ______.
The general solution of the equation tan2 x = 1 is ______.
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 ______.
Find the general solution of sin θ + sin 3θ + sin 5θ = 0
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 ______.
