Advertisements
Advertisements
प्रश्न
State whether the following equation has a solution or not?
3 sin θ = 5
उत्तर
∴ sin θ = `5/3`
This is possible because sin θ is any real number.
∴ 3 sin θ = 5 has a solution.
This is not possible because -1 ≤ sin θ ≤ 1 for any θ.
∴ 3 sin θ = 5 does not have any solution.
APPEARS IN
संबंधित प्रश्न
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 principal solution of the following equation:
`sqrt(3)` cosecθ + 2 = 0
Find the general solution of the following equation:
tan `(2θ)/(3) = sqrt3`.
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:
In Δ ABC if ∠A = 45°, ∠B = 30°, then the ratio of its sides are
Select the correct option from the given alternatives:
If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______
Select the correct option from the given alternatives:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
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:
sin 2θ = `-1/2`
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:
`tan^2 theta = 3`
Show that `tan^-1 1/2 - tan^-1 1/4 = tan^-1 2/9`.
Show that `cos^-1 sqrt3/2 + 2 sin^-1 sqrt3/2 = (5pi)/6`.
Prove the following:
`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0
The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______
Find the principal solutions of sin x − 1 = 0
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
`cos^-1 (cos (4pi)/3)` = ______.
`int 1/(sin x * cos x)` dx = ?
The general solution of sec θ = `sqrt2` is
If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is
If f(x) = sin-1`(sqrt((1 - x)/2))`, then f'(x) = ?
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
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 the equation tan θ tan 2θ = 1 is given by ______
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 ______.
If y = `(2sinα)/(1 + cosα + sinα)`, then value of `(1 - cos α + sin α)/(1 + sin α)` is ______.
The general solution of x(1 + y2)1/2 dx + y(1 + x2)1/2 dy = 0 is ______.
General solution of the equation sin 2x – sin 4x + sin 6x = 0 is ______.
Which of the following equation has no solution?
The general solution of the equation tan2 x = 1 is ______.
The general solution to cos100x – sin100x = 1 is ______.