Advertisements
Advertisements
प्रश्न
Find the principal solutions of tan x = `-sqrt(3)`
Advertisements
उत्तर
tan x = `-sqrt(3)`
∴ tan x = `-tan (pi/3)`
∴ tan x = `tan (pi - pi/3)`
= `tan ((2pi)/3)` and tan x = `tan (2pi - pi/3)`
= `tan ((5pi)/3)`
such that `0 ≤ (2pi)/3 < 2pi` and `0 ≤ (5pi)/3 < 2pi`
∴ The required principal solutions are x = `(2pi)/3` and x = `(5pi)/3`.
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation:
cosθ = `(1)/(2)`
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:
sinθ = `1/2`.
Find the general solution of the following equation :
cosθ = `sqrt(3)/(2)`
Find the general solution of the following equation:
cot θ = 0.
Find the general solution of the following equation:
cos 4θ = cos 2θ
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 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 = ____.
Select the correct option from the given alternatives:
The value of cot (tan-12x + cot-12x) is
Find the principal solutions of the following equation:
sin 2θ = `-1/2`
Find the principal solutions of the following equation:
tan 3θ = - 1
Find the principal solutions of the following equation:
cot θ = 0
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.
Show that `cos^-1 sqrt3/2 + 2 sin^-1 sqrt3/2 = (5pi)/6`.
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
If sin-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos-1 x is _______.
`cos^-1 (cos (4pi)/3)` = ______.
`int 1/(sin x * cos x)` dx = ?
`int (sin (log x))^2/x` log x dx = ?
If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is
`[sin (tan^-1 3/4)]^2 + [sin(tan^-1 4/3)]^2 = ?`
If 2 cos2 θ + 3 cos θ = 2, then permissible value of cos θ is ________.
Which of the following equations has no solution?
The value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` is ______.
The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 is ______
If sin θ + cos θ = 1, then the general value of θ is ______.
The general solution of cosec x = `-sqrt2` is ______
The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval `[pi/2, (3pi)/2]` 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 ______.
If a = sin θ + cos θ, b = sin3 θ + cos3 θ, then ______.
With usual notations, in any ΔABC, if a cos B = b cos A, then the triangle is ______.
The general solution of cot 4x = –1 is ______.
If tan θ + sec θ = `sqrt(3)`, find the general value of θ.
