Advertisements
Advertisements
Question
Find the principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
Advertisements
Solution
`sqrt(3)` cosec θ + 2 = 0
`sqrt(3)` cosec θ = - 2
cosec θ = `(-2)/sqrt(3)`
sin θ = `-sqrt(3)/(2)`
sin θ = `-sin(pi/3)`
sin θ = `sin(pi + pi/3)` and sin θ = `sin (2pi - pi/3)`
sin θ = `sin ((4pi)/3)` and sin θ = `sin ((5pi)/3)`
= `[therefore 0≤ (4pi)/3 < 2pi and 0≤ (5pi)/3< 2pi]`
θ = `(4pi)/(3)` and θ = `(5pi)/(3)`
Principal solutions one `(4pi)/(3)` and `(5pi)/(3)`.
APPEARS IN
RELATED QUESTIONS
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 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:
4sin2θ = 1.
Find the general solution of the following equation:
sin θ = tan θ
State whether the following equation have solution or not?
3 tanθ = 5
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 sin θ = `- 1/2` 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 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 = ____.
If in a triangle, the angles are in A.P. and b: c = `sqrt3: sqrt2`, then A is equal to
`"cos"^-1 ("cos" (7pi)/6)` = _________.
Select the correct option from the given alternatives:
The value of cot (tan-12x + cot-12x) is
The principal value of sin–1 `(- sqrt3/2)` is ______.
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) =` _____
`cos[tan^-1 1/3 + tan^-1 1/2]` = ______
Find the general solutions of the following equation:
`tan^2 theta = 3`
With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`
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`
Prove the following:
`cos^-1 "x" = tan^-1 (sqrt(1 - "x"^2)/"x")`, if x > 0
Prove the following:
`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0
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`
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 = `-1/2`
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
`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 f(x) = sin-1`(sqrt((1 - x)/2))`, then f'(x) = ?
If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?
The number of solutions of `sin^2 theta = 1/2` in [0, π] is ______.
If function
f(x) = `x - |x|/x, x < 0`
= `x + |x|/x, x > 0`
= 1, x = 0, then
If 4 sin-1x + 6 cos-1 x = 3π then x = ______.
The general value of θ in the equation `2sqrt(3) cos theta = tan theta` is ______.
Find the principal solutions of cot θ = 0
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
Which of the following equation has no solution?
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.
