Advertisements
Advertisements
प्रश्न
Show that `tan^-1 1/2 = 1/3 tan^-1 11/2`
उत्तर
We have to show that
`tan^-1 1/2 = 1/3 tan^-1 11/2`
i.e. to show that `3 tan^-1 1/2 = tan^-1 11/2`
LHS = `3 tan^-1 1/2`
`= 2 tan^-1 1/2 + tan^-1 1/2`
`= tan^-1 [(2 xx 1/2)/(1 - (1/2)^2)] + tan^-1 1/2 .....[∵ 2tan^-1 "x" = tan^-1 ("2x"/"1 - x"^2)]`
`= tan^-1 [1/(3/4)] + tan^-1 1/2`
`= tan^-1 4/3 + tan^-1 1/2`
`= tan^-1 [(4/3 + 1/2)/(1 - 4/3 xx 1/2)]`
`= tan^-1 ((8 + 3)/(6 - 4))`
`= tan^-1 (11/2)` = RHS
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation:
cosθ = `(1)/(2)`
Find the principal solution of the following equation:
cot θ = 0
Find the general solution of the following equation :
cosθ = `sqrt(3)/(2)`
Find the general solution of the following equation:
cot θ = 0.
Find the general solution of the following equation:
4cos2θ = 3.
State whether the following equation has a solution or not?
cos2θ = – 1.
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
If `sqrt3`cos x - sin x = 1, then general value of x is ______.
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:
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 `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______
`"cos"["tan"^-1 1/3 + "tan"^-1 1/2]` = ______
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:
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 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.
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
The general solution of sec θ = `sqrt2` is
If f(x) = sin-1`(sqrt((1 - x)/2))`, then f'(x) = ?
The number of solutions of `sin^2 theta = 1/2` in [0, π] is ______.
The value of θ in (π, 2π) satisfying the equation sin2θ - cos2θ = 1 is ______
The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 is ______
If sin θ + cos θ = 1, then the general value of θ is ______.
The general solution of cot θ + tan θ = 2 is ______.
The equation 3sin2x + 10 cos x – 6 = 0 is satisfied, if ______.
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 ______.
The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ is ______.
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
The general solution of the equation tan2 x = 1 is ______.
If a = sin θ + cos θ, b = sin3 θ + cos3 θ, then ______.
