Advertisements
Advertisements
प्रश्न
Find the general solution of the following equation:
cot θ = 0.
Advertisements
उत्तर
The general solution of tan θ = tan α is
θ = nπ + α, n ∈ Z
Now, cot θ = 0
∴ tan θ does not exist
∴ tan θ = `tan pi/(2) ...[∵ tan pi/(2)` does not exist]
∴ the required general solution is
θ = nπ + `pi/(2)`, n ∈ Z.
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
Find the general solution of the following equation:
sinθ = `1/2`.
Find the general solution of the following equation:
tan θ = `(1)/(sqrt(3))`
Find the general solution of the following equation:
tan θ = - 1
Find the general solution of the following equation:
4 cos2 θ = 3
Find the general solution of the following equation:
cos 4θ = cos 2θ
Find the general solution of the following equation:
cosθ + sinθ = 1.
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 the usual notations prove that `2{asin^2 "C"/(2) + "c"sin^2 "A"/(2)}` = a – b + c.
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 cot θ = `sqrt3` 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:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
The principal value branch of sec-1x is ______.
Select the correct option from the given alternatives:
In any ΔABC, if acos B = bcos A, then the triangle is
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^2 theta = 3`
Find the general solutions of the following equation:
sin θ - cos θ = 1
In ΔABC, prove that `("a - b")^2 cos^2 "C"/2 + ("a + b")^2 sin^2 "C"/2 = "c"^2`
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.
Prove the following:
`cos^-1 "x" = tan^-1 (sqrt(1 - "x"^2)/"x")`, if x > 0
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 cos-1 x + cos-1y + cos-1z = 3π, then show that x2 + y2 + z2 + 2xyz = 1.
Find the principal solutions of cosec x = 2
Find the principal solutions of cos 2𝑥 = 1
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
`cos^-1 (cos (4pi)/3)` = ______.
`int 1/(sin x * cos x)` dx = ?
If f(x) = sin-1`(sqrt((1 - x)/2))`, then f'(x) = ?
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
The number of solutions of `sin^2 theta = 1/2` in [0, π] 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 ______
The general solution of 4sin2 x = 1 is ______.
The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval `[pi/2, (3pi)/2]` is ______.
Find the principal solutions of cot θ = 0
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 ______.
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
If `sin^-1 4/5 + cos^-1 12/13` = sin–1α, then find the value of α.
If tan3θ = cotθ, then θ =
