Advertisements
Advertisements
Question
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
Advertisements
Solution
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
RELATED QUESTIONS
Find the principal solution of the following equation:
Sec θ = `(2)/sqrt(3)`
Find the principal solution of the following equation:
cot θ = 0
Find the general solution of the following equation:
sinθ = `1/2`.
Find the general solution of the following equation:
cot θ = 0.
Find the general solution of the following equation:
sin 2θ = `1/2`
Find the general solution of the following equation:
sin θ = tan θ
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:
The principal solutions of equation cot θ = `sqrt3` are ______.
Select the correct option from the given alternatives:
The general solution of sec x = `sqrt(2)` is ______.
If `sqrt3 cos x − sin x = 1`, then general value of x is ______.
Select the correct option from the given alternatives:
In ΔABC if c2 + a2 – b2 = ac, then ∠B = ____.
If in a triangle, the angles are in A.P. and b: c = `sqrt3: sqrt2`, then A is equal to
`"cos"^-1 ("cos" (7pi)/6)` = _________.
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 ______.
Find the principal solutions of the following equation:
sin 2θ = `-1/2`
Find the general solutions of the following equation:
`tan theta = - sqrt3`
Find the general solutions of the following equation:
sin θ - cos θ = 1
In ΔABC, prove that `("a - b")^2 cos^2 "C"/2 + ("a + b")^2 sin^2 "C"/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`
Show that `cos^-1 sqrt3/2 + 2 sin^-1 sqrt3/2 = (5pi)/6`.
Show that `2 cot^(-1) 3/2 + sec^(-1) 13/12 = π/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 `tan^-1 "x" + tan^-1 "y" + tan^-1 "z" = pi/2,` then show that xy + yz + zx = 1
If cos-1 x + cos-1y + cos-1z = 3π, then show that x2 + y2 + z2 + 2xyz = 1.
Find the principal solutions of cos 2𝑥 = 1
`int 1/(sin x * cos x)` dx = ?
`int (sin (log x))^2/x` log x dx = ?
`[sin (tan^-1 3/4)]^2 + [sin(tan^-1 4/3)]^2 = ?`
If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?
The value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` is ______.
The number of solutions of cos 2θ = sin θ in (0, 2π) is ______
The value of θ in (π, 2π) satisfying the equation sin2θ - cos2θ = 1 is ______
The general solution of the equation tan θ tan 2θ = 1 is given by ______
Which of the following is true in a triangle ABC?
Which of the following equation has no solution?
The general solution of the equation tan2 x = 1 is ______.
The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x 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 `sin^-1 4/5 + cos^-1 12/13` = sin–1α, then find the value of α.
