Advertisements
Advertisements
Question
Find the principal solution of the following equation:
cot θ = 0
Advertisements
Solution
The given equation is cot θ = 0 which is same as
tan θ = ∞
We know that,
tan `π/2` = ∞ and tan (π + θ) = tan θ
∴ `tan (π/2) = tan (π + π/2) = tan ((3π)/2)`
∴ `tan (π/2) = tan ((3π)/2) = ∞`, where,
`0 < π/2 < 2π and 0 < (3π)/2 < 2π`
∴ cot θ = 0, i.e., tan θ = ∞ gives
`tan θ = tan (π/2) = tan ((3π)/2)`
∴ `θ = π/2 "and" θ = (3π)/2`
Hence, the required principal solution are `θ = π/2 "and" θ = (3π)/2`.
Notes
Answer in the textbook is incorrect.
APPEARS IN
RELATED QUESTIONS
Find the principal solution of the following equation:
tan θ = – 1
Find the principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
Find the general solution of the following equation:
tan θ = `(1)/(sqrt(3))`
Find the general solution of the following equation:
cot 4θ = – 1
Find the general solution of the following equation:
sin θ = tan θ
State whether the following equation have solution or not?
cos 2θ = – 1
State whether the following equation has a solution or not?
cos2θ = – 1.
With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c2 .
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:
If polar coordinates of a point are `(2, pi/4)`, then its cartesian coordinates are
Select the correct option from the given alternatives:
In ΔABC if c2 + a2 – b2 = ac, then ∠B = ____.
If in a triangle, the angles are in A.P. and b: c = `sqrt3: sqrt2`, then A is equal to
Select the correct option from the given alternatives:
If tan-1(2x) + tan-1(3x) = `pi/4`, then x = _____
Select the correct option from the given alternatives:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
Find the general solutions of the following equation:
sin θ - cos θ = 1
In Δ ABC, if cos A = sin B - cos C then show that it is a right-angled triangle.
If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.
State whether the following equation has a solution or not?
3 sin θ = 5
If tan-12x + tan-13x = `pi/4`, then find the value of x.
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 cos 2𝑥 = 1
Find the principal solutions of sin x = `-1/2`
`cos^-1 (cos (4pi)/3)` = ______.
The value of tan 57°- tan 12°- tan 57° tan 12° is ______.
`int 1/(sin x * cos x)` dx = ?
If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?
The principal solutions of cot x = `sqrt3` are ______.
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
The number of solutions of cos 2θ = sin θ in (0, 2π) is ______
If function
f(x) = `x - |x|/x, x < 0`
= `x + |x|/x, x > 0`
= 1, x = 0, then
The value of θ in (π, 2π) satisfying the equation sin2θ - cos2θ = 1 is ______
The general solution of sin 2x = cos 2x is ______
The general solution of the equation tan θ tan 2θ = 1 is given by ______
The general solution of cot θ + tan θ = 2 is ______.
The general solution of 4sin2 x = 1 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 number of principal solutions of tan 2θ = 1 is ______.
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.
The general solution of cot 4x = –1 is ______.
If `sin^-1 4/5 + cos^-1 12/13` = sin–1α, then find the value of α.
