Advertisements
Advertisements
प्रश्न
Find the principal solutions of cot θ = 0
Advertisements
उत्तर
Given, cot θ = 0
Since, cot θ ∈ (0, 2π)
∴ cot θ = 0 = `cot π/2 = cot(π + π/2)` ......[∵ cot (π + θ) = cot θ]
∴ cot θ = `cot π/2 = cot (3π)/2`
∴ θ = `π/2` or θ = `(3π)/2`
Hence, the required principal solutions are `{π/2, (3π)/2}`
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation:
cosθ = `(1)/(2)`
Find the principal solution of the following equation:
cot θ = 0
Find the principal solution of the following equation:
sin θ = `-1/2`
Find the principal solution of the following equation:
tan θ = – 1
Find the general solution of the following equation :
cosθ = `sqrt(3)/(2)`
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:
4 cos2 θ = 3
Find the general solution of the following equation:
4sin2θ = 1.
Find the general solution of the following equation:
cos 4θ = cos 2θ
Find the general solution of the following equation:
sin θ = tan θ
Find the general solution of the following equation:
tan3θ = 3 tanθ.
With the usual notations prove that `2{asin^2 "C"/(2) + "c"sin^2 "A"/(2)}` = a – b + c.
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:
If cos pθ = cos qθ, p ≠ q, then ______.
Select the correct option from the given alternatives:
In ΔABC if c2 + a2 – b2 = ac, then ∠B = ____.
Select the correct option from the given alternatives:
In ΔABC, ac cos B - bc cos A = _______
Select the correct option from the given alternatives:
`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______
The principal value branch of sec-1x is ______.
Find the principal solutions of the following equation:
sin 2θ = `-1/2`
Find the general solutions of the following equation:
`tan theta = - sqrt3`
With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`
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 x, y, z are positive, then prove that
`tan^-1 (("x - y")/(1 + "xy")) + tan^-1 (("y - z")/(1 + "yz")) + tan^-1 (("z - x")/(1 + "zx")) = 0`
The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______
If sin-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos-1 x is _______.
`int 1/(sin x * cos x)` dx = ?
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
Which of the following equations has no solution?
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 value of θ in the equation `2sqrt(3) cos theta = tan theta` is ______.
The general solution of x(1 + y2)1/2 dx + y(1 + x2)1/2 dy = 0 is ______.
Which of the following equation has no solution?
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
The general solution of the equation tan2 x = 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.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
If tan3θ = cotθ, then θ =
