Advertisements
Advertisements
प्रश्न
Find the general solution of sin θ + sin 3θ + sin 5θ = 0
Advertisements
उत्तर
We have sin θ + sin 3θ + sin 5θ = 0
∴ (sin θ + sin 5θ) + sin 3θ = 0
∴ 2 sin 3θ × cos 2θ + sin 3θ = 0
∴ (2 cos 2θ + 1) sin 3θ = 0
∴ sin 3θ = 0 or cos 2θ = `-1/2`
∴ sin 3θ = 0 or cos 2θ = `cos (2π)/3`
∴ 3θ = nπ or 2θ = `2nπ ± (2π)/3`, where n ∈ Z.
θ = `(nπ)/3` or θ = `nπ ± π/3`,
where n ∈ Z is the required general solution.
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:
cosec θ = - √2.
Find the general solution of the following equation:
tan θ = - 1
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:
cot 4θ = – 1
Find the general solution of the following equation:
cos 4θ = cos 2θ
Find the general solution of the following equation:
cosθ + sinθ = 1.
In Δ ABC, prove that a3 sin(B – C) + b3sin(C – A) + c3sin(A – B) = 0
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:
The principal solutions of equation cot θ = `sqrt3` are ______.
Select the correct option from the given alternatives:
If polar coordinates of a point are `(2, pi/4)`, then its cartesian coordinates are
`"cos"^-1 ("cos" (7pi)/6)` = _________.
The principal value of sin–1 `(- sqrt3/2)` is ______.
`cos[tan^-1 1/3 + tan^-1 1/2]` = ______
Find the principal solutions of the following equation:
sin 2θ = `-1/2`
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, if cos A = sin B - cos C then show that it is a right-angled triangle.
State whether the following equation has a solution or not?
3 sin θ = 5
If 2 tan-1(cos x) = tan-1(2 cosec x), then find the value of x.
If tan-12x + tan-13x = `pi/4`, then find the value of x.
Show that `tan^-1 1/2 - tan^-1 1/4 = tan^-1 2/9`.
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 cos 2𝑥 = 1
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is
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 values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
Which of the following equations has no solution?
The number of solutions of cos 2θ = sin θ in (0, 2π) is ______
If function
f(x) = `x - |x|/x, x < 0`
= `x + |x|/x, x > 0`
= 1, x = 0, then
The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 is ______
The general solution of the equation tan θ tan 2θ = 1 is given by ______
The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval `[pi/2, (3pi)/2]` is ______.
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ is ______.
The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.
The general solution to cos100x – sin100x = 1 is ______.
The general solution of cot 4x = –1 is ______.
If tan3θ = cotθ, then θ =
