Advertisements
Advertisements
प्रश्न
If tan-12x + tan-13x = `pi/4`, then find the value of x.
Advertisements
उत्तर
tan-12x + tan-13x = `pi/4`
∴ `tan^-1 ((2"x" + 3"x")/(1 - "2x" xx "3x")) = pi/4`, where 2x > 0, 3x > 0
∴ `"5x"/(1 - "6x"^2) = tan pi/4 = 1`
∴ 5x = 1 - 6x2
∴ 6x2 + 5x - 1 = 0
∴ 6x2 + 6x - x - 1 = 0
∴ 6x(x + 1) - 1(x + 1) = 0
∴ (x + 1)(6x - 1) = 0
∴ x = -1 or x = `1/6`
But x > 0 ∴ x ≠ - 1
Hence, x = `1/6`
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:
sinθ = `1/2`.
Find the general solution of the following equation:
cosec θ = - √2.
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.
If in a triangle, the angles are in A.P. and b: c = `sqrt3: sqrt2`, then A is equal to
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) =` _____
`cos[tan^-1 1/3 + tan^-1 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`
If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.
If 2 tan-1(cos x) = tan-1(2 cosec x), then find the value of x.
Show that `tan^-1 1/2 = 1/3 tan^-1 11/2`
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
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))`
Find the principal solutions of cosec x = 2
Find the principal solutions of sin x = `-1/2`
The general solution of sec θ = `sqrt2` is
`int (sin (log x))^2/x` log x dx = ?
`[sin (tan^-1 3/4)]^2 + [sin(tan^-1 4/3)]^2 = ?`
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
Which of the following equations has no solution?
The value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` is ______.
If 4 sin-1x + 6 cos-1 x = 3π then x = ______.
The general solution of sin 2x = cos 2x is ______
The general solution of the equation tan θ tan 2θ = 1 is given by ______
The general solution of cot θ + tan θ = 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 ______.
General solution of the equation sin 2x – sin 4x + sin 6x = 0 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 ______.
Find the general solution of sin θ + sin 3θ + sin 5θ = 0
Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.
If tan θ + sec θ = `sqrt(3)`, find the general value of θ.
