Advertisements
Advertisements
Question
State whether the following equation has a solution or not?
2sinθ = 3
Advertisements
Solution
2sinθ = 3
∴ sinθ = `(3)/(2)`
This is not possible because – 1 ≤ sinθ ≤ 1 for any θ.
∴ 2 sinθ = 3 does not have any solution.
APPEARS IN
RELATED QUESTIONS
Find the principal solution of the following equation:
cot θ = 0
Find the principal solution of the following equation:
sin θ = `-1/2`
Find the general solution of the following equation:
sinθ = `1/2`.
Find the general solution of the following equation:
cot θ = 0.
Find the general solution of the following equation:
sin 2θ = `1/2`
Find the general solution of the following equation:
cot 4θ = – 1
Find the general solution of the following equation:
4 cos2 θ = 3
Find the general solution of the following equation:
4sin2θ = 1.
Find the general solution of the following equation:
cos 4θ = cos 2θ
Find the general solution of the following equation:
sin θ = tan θ
State whether the following equation have solution or not?
cos 2θ = – 1
In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.
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.
Select the correct option from the given alternatives:
If polar coordinates of a point are `(2, pi/4)`, then its cartesian coordinates are
If `sqrt3`cos x - sin x = 1, then general value of x is ______.
If in a triangle, the angles are in A.P. and b: c = `sqrt3: sqrt2`, then A is equal to
The principal value of sin–1 `(- sqrt3/2)` is ______.
If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______.
Select the correct option from the given alternatives:
`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______
If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is ______.
Find the principal solutions of the following equation:
tan 3θ = - 1
Find the general solutions of the following equation:
`tan theta = - sqrt3`
In Δ ABC, if cos A = sin B - cos C then show that it is a right-angled triangle.
If sin-1(1 - x) - 2 sin-1x = `pi/2`, then find the value of x.
If tan-12x + tan-13x = `pi/4`, then find the value of x.
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 `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.
If sin-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos-1 x is _______.
`cos^-1 (cos (4pi)/3)` = ______.
The value of tan 57°- tan 12°- tan 57° tan 12° is ______.
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 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 sin 2x = cos 2x is ______
The general solution of cot θ + tan θ = 2 is ______.
The general solution of x(1 + y2)1/2 dx + y(1 + x2)1/2 dy = 0 is ______.
The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ is ______.
General solution of the equation sin 2x – sin 4x + sin 6x = 0 is ______.
The general solution of the equation tan2 x = 1 is ______.
The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.
If tan θ + sec θ = `sqrt(3)`, find the general value of θ.
