Advertisements
Advertisements
प्रश्न
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
उत्तर
As we know that
2 tan–1(x) = `tan^-1 ((2x)/(1 - x^2))`
∴ 2 tan–1(cos x) = `tan^-1 ((2 cos x)/(1 - cos^2x))`
⇒ 2 tan–1(cos x) = `tan^-1 ((2 cos x)/(sin^2x))`
Given, 2 tan–1 (cos x) = tan–1 (2 cosec x)
∴ `tan^-1 ((2 cos x)/(sin^2x))` = tan–1 (2 cosec x) ......[From (i)]
⇒ `(2 cos x)/sin^2x `= 2 cosec x
⇒ `cosx/sin^2x = 1/sinx`
⇒ cos x = sin x
⇒ x = `π/4`
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation:
Sec θ = `(2)/sqrt(3)`
Find the general solution of the following equation:
cosec θ = - √2.
Find the general solution of the following equation:
cos 4θ = cos 2θ
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.
With the usual notations prove that `2{asin^2 "C"/(2) + "c"sin^2 "A"/(2)}` = a – b + c.
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 sin θ = `- 1/2` are ______.
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:
In ΔABC if c2 + a2 – b2 = ac, then ∠B = ____.
Select the correct option from the given alternatives:
In ΔABC, ac cos B - bc cos A = _______
`"cos"^-1 ("cos" (7pi)/6)` = _________.
Select the correct option from the given alternatives:
The value of cot (tan-12x + cot-12x) is
Select the correct option from the given alternatives:
If tan-1(2x) + tan-1(3x) = `pi/4`, then x = _____
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:
The principal value branch of sec-1x is
`"cos"["tan"^-1 1/3 + "tan"^-1 1/2]` = ______
Select the correct option from the given alternatives:
In any ΔABC, if acos B = bcos A, then the triangle is
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 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`.
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
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 x, y, z are positive, then prove that
`tan^-1 (("x - y")/(1 + "xy")) + tan^-1 (("y - z")/(1 + "yz")) + tan^-1 (("z - x")/(1 + "zx")) = 0`
Find the principal solutions of cosec x = 2
If cos–1x + cos–1y – cos–1z = 0, 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 _______.
The value of tan 57°- tan 12°- tan 57° tan 12° is ______.
The general solution of sec θ = `sqrt2` is
If f(x) = sin-1`(sqrt((1 - x)/2))`, then f'(x) = ?
If 2 cos2 θ + 3 cos θ = 2, then permissible value of cos θ is ________.
The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.
The general solution of 4sin2 x = 1 is ______.
The general value of θ in the equation `2sqrt(3) cos theta = tan theta` 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 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 ______.
Find the general solution of sin θ + sin 3θ + sin 5θ = 0
If `2sin^-1 3/7` = cos–1β, then find the value of β.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
