Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
tan θ = - 1
Advertisements
उत्तर
The general solution of tan θ = tan α is
θ = nπ + α, n ∈ Z.
Now, tan θ = – 1
∴ tan θ = - tan `pi/(4) .....[ ∵ tan pi/4 = 1]`
∴ tan θ = `tan(pi - pi/4)` ...[ ∵ tan(π - θ) = – tan θ]
∴ tan θ = `tan (3pi)/(4)`
∴ the required general solution is
θ = nπ + `(3pi)/(4)`, n ∈ Z.
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation:
Sec θ = `(2)/sqrt(3)`
Find the general solution of the following equation:
sinθ = `1/2`.
Find the general solution of the following equation:
sec θ = `sqrt(2)`.
Find the general solution of the following equation:
4sin2θ = 1.
Find the general solution of the following equation:
cos 4θ = cos 2θ
State whether the following equation has a solution or not?
2sinθ = 3
State whether the following equation have solution or not?
3 tanθ = 5
In ΔABC, prove that `sin(("B" − "C")/2) = (("b" − "c")/"a")cos "A"/(2)`.
`"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) =` _____
If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is ______.
Find the general solutions of the following equation:
`tan theta = - sqrt3`
If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.
Show that `tan^-1 1/2 - tan^-1 1/4 = tan^-1 2/9`.
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
If | x | < 1, then prove that
`2 tan^-1 "x" = tan^-1 ("2x"/(1 - "x"^2)) = sin^-1 ("2x"/(1 + "x"^2)) = cos^-1 ((1 - "x"^2)/(1 + "x"^2))`
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 cos-1 x + cos-1y + cos-1z = 3π, then show that x2 + y2 + z2 + 2xyz = 1.
The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______
Find the principal solutions of cosec x = 2
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
`int (sin (log x))^2/x` log x dx = ?
If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is
The number of solutions of `sin^2 theta = 1/2` in [0, π] is ______.
If 4 sin-1x + 6 cos-1 x = 3π then x = ______.
The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 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 cosec x = `-sqrt2` is ______
The equation 3sin2x + 10 cos x – 6 = 0 is satisfied, if ______.
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
The general solution of x(1 + y2)1/2 dx + y(1 + x2)1/2 dy = 0 is ______.
Which of the following equation has no solution?
If a = sin θ + cos θ, b = sin3 θ + cos3 θ, then ______.
Find the general solution of sin θ + sin 3θ + sin 5θ = 0
Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.
If tan3θ = cotθ, then θ =
