Advertisements
Advertisements
प्रश्न
Find the principal solutions of the following equation:
cot θ = 0
उत्तर
cot θ = 0
Since θ ∈ (0, 2π)
∴ cot θ = 0 = cot `π/2 = "cot" (π + pi/2)` … [∴ cot (π + θ) = cot θ]
∴ cot θ = cot `π/2 = cot (3π)/2`
∴ `θ = pi/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:
Sec θ = `(2)/sqrt(3)`
Find the principal solution of the following equation:
sin θ = `-1/2`
Find the principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
Find the general solution of the following equation:
4cos2θ = 3.
In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.
In Δ ABC, prove that a3 sin(B – C) + b3sin(C – A) + c3sin(A – B) = 0
Select the correct option from the given alternatives:
The principal solutions of equation sin θ = `- 1/2` are ______.
Select the correct option from the given alternatives:
The principal solutions of equation cot θ = `sqrt3` are ______.
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 = ______
Select the correct option from the given alternatives:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
`"cos"["tan"^-1 1/3 + "tan"^-1 1/2]` = ______
Find the general solutions of the following equation:
`tan theta = - sqrt3`
Find the general solutions of the following equation:
sin2 θ - cos2 θ = 1
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 tan-12x + tan-13x = `pi/4`, then find the value of x.
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
Find the principal solutions of tan x = `-sqrt(3)`
If sin-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos-1 x is _______.
`cos^-1 (cos (4pi)/3)` = ______.
The value of tan 57°- tan 12°- tan 57° tan 12° is ______.
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?
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?
If function
f(x) = `x - |x|/x, x < 0`
= `x + |x|/x, x > 0`
= 1, x = 0, then
The general solution of cot θ + tan θ = 2 is ______.
The general solution of 4sin2 x = 1 is ______.
The general solution of cosec x = `-sqrt2` is ______
The equation 3sin2x + 10 cos x – 6 = 0 is satisfied, if ______.
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 ______.
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 ______.
