Advertisements
Advertisements
प्रश्न
If 2 tan-1(cos x) = tan-1(2 cosec x), then find the value of x.
Advertisements
उत्तर
2 tan-1(cos x) = tan-1(2 cosec x)
∴ `tan^-1 [(2 cos "x")/(1 - cos^2"x")] = tan^-1 (2 "cosec x") ...[because 2 tan^-1 "x" = tan^-1 ("2x"/(1 - "x"^2))]`
∴ `(2 "cos x")/(1 - cos^2 "x") = 2 "cosec x"`
∴ `(2 "cos x")/(sin^2 "x") = 2/ "sin x"`
∴ cos x = sin x
∴ x = `pi/4` ....`[because sin pi/4 = cos pi/4]`
APPEARS IN
संबंधित प्रश्न
Find the principal solution of the following equation:
Sec θ = `(2)/sqrt(3)`
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.
Find the general solution of the following equation:
tan θ = - 1
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:
cosθ + sinθ = 1.
State whether the following equation has a solution or not?
cos2θ = – 1.
State whether the following equation has a solution or not?
2sinθ = 3
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
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:
The principal solutions of equation cot θ = `sqrt3` are ______.
If `sqrt3 cos x − sin x = 1`, then general value of x is ______.
`"cos"^-1 ("cos" (7pi)/6)` = _________.
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:
sin2 θ - cos2 θ = 1
With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
Show that `tan^-1 1/2 = 1/3 tan^-1 11/2`
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 cos-1 x + cos-1y + cos-1z = 3π, then show that x2 + y2 + z2 + 2xyz = 1.
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
`int (sin (log x))^2/x` log x dx = ?
The number of solutions of `sin^2 theta = 1/2` in [0, π] is ______.
The value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` is ______.
The value of θ in (π, 2π) satisfying the equation sin2θ - cos2θ = 1 is ______
The general solution of sin 2x = cos 2x is ______
If sin θ + cos θ = 1, then the general value of θ is ______.
The equation 3sin2x + 10 cos x – 6 = 0 is satisfied, if ______.
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?
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 ______.
Prove that the general solution of cos θ = cos α is θ = 2nπ ± α, n ∈ Z.
The general solution to cos100x – sin100x = 1 is ______.
If `sin^-1 4/5 + cos^-1 12/13` = sin–1α, then find the value of α.
