Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
tan θ = `(1)/(sqrt(3))`
Advertisements
उत्तर
The general solution of tan θ = tan α is
θ = nπ + α, n ∈ Z
Now,
`tan θ = 1/(sqrt(3)) = tan π/6 ...[∵ tan π/6 = 1/(sqrt(3))]`
∴ the required general solution is
θ = nπ + `pi/(6)`, n ∈ Z.
APPEARS IN
संबंधित प्रश्न
Find the general solution of the following equation:
sec θ = `sqrt(2)`.
Find the general solution of the following equation:
cosec θ = - √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:
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.
With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c2 .
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 = ____.
`"cos"^-1 ("cos" (7pi)/6)` = _________.
If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______.
Find the principal solutions of the following equation:
tan 3θ = - 1
Find the principal solutions of the following equation:
cot θ = 0
Find the general solutions of the following equation:
`tan theta = - sqrt3`
Find the general solutions of the following equation:
sin θ - cos θ = 1
In Δ ABC, prove that `cos(("A" - "B")/2) = (("a" + "b")/"c")sin "C"/2` .
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`
If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.
If 2 tan-1(cos x) = tan-1(2 cosec x), then find the value of x.
If sin-1(1 - x) - 2 sin-1x = `pi/2`, then find the value of x.
Prove the following:
`cos^-1 "x" = tan^-1 (sqrt(1 - "x"^2)/"x")`, if x > 0
If `tan^-1 "x" + tan^-1 "y" + tan^-1 "z" = pi/2,` then show that xy + yz + zx = 1
If cos-1 x + cos-1y + cos-1z = 3π, then show that x2 + y2 + z2 + 2xyz = 1.
Find the principal solutions of tan x = `-sqrt(3)`
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
The value of tan 57°- tan 12°- tan 57° tan 12° is ______.
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
The general solution of sec θ = `sqrt2` is
`int (sin (log x))^2/x` log x dx = ?
`[sin (tan^-1 3/4)]^2 + [sin(tan^-1 4/3)]^2 = ?`
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
The value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` 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 solution of 4sin2 x = 1 is ______.
The general solution of cosec x = `-sqrt2` is ______
The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ is ______.
The number of principal solutions of tan 2θ = 1 is ______.
The general solution of the equation tan2 x = 1 is ______.
Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.
If `sin^-1 4/5 + cos^-1 12/13` = sin–1α, then find the value of α.
If tan θ + sec θ = `sqrt(3)`, find the general value of θ.
If tan3θ = cotθ, then θ =
