Advertisements
Advertisements
Question
Show that `cot^-1 1/3 - tan^-1 1/3 = cot^-1 3/4`.
Advertisements
Solution
LHS = `cot^-1 1/3 - tan^-1 1/3`
`= tan^-1 3 - tan^-1 1/3 ....[because cot^-1 "x" = tan^-1 (1/"x")]`
`= tan^-1 [(3 - 1/3)/(1 + 3(1/3))]`
`= tan^-1 [(8/3)/(1 + 1)]`
`= tan^-1 (4/3)`
`= cot^-1 (3/4) ....[tan^-1 "x" = cot^-1 (1/"x")]`
= RHS.
APPEARS IN
RELATED QUESTIONS
Find the principal solution of the following equation :
cot θ = `sqrt(3)`
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:
sin 2θ = `1/2`
Find the general solution of the following equation:
4 cos2 θ = 3
Find the general solution of the following equation:
tan3θ = 3 tanθ.
In ΔABC, prove that `sin(("B" − "C")/2) = (("b" − "c")/"a")cos "A"/(2)`.
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:
If polar coordinates of a point are `(2, pi/4)`, then its cartesian coordinates 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 = _______
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:
`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____
`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 general solutions of the following equation:
`tan theta = - sqrt3`
Find the general solutions of the following equation:
sin2 θ - cos2 θ = 1
In Δ ABC, prove that `cos(("A" - "B")/2) = (("a" + "b")/"c")sin "C"/2` .
In Δ ABC, if cos A = sin B - cos C then show that it is a right-angled triangle.
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 `2 cot^(-1) 3/2 + sec^(-1) 13/12 = π/2`
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`
If `tan^-1 "x" + tan^-1 "y" + tan^-1 "z" = pi/2,` then show that xy + yz + zx = 1
Find the principal solutions of sin x = `-1/2`
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 _______.
`cos^-1 (cos (4pi)/3)` = ______.
The value of tan 57°- tan 12°- tan 57° tan 12° is ______.
If 2 cos2 θ + 3 cos θ = 2, then permissible value of cos θ 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 ______.
The value of sin 18° is ______.
The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 is ______
If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.
Find the principal solutions of cot θ = 0
If 2 tan–1(cos x) = tan–1(2 cosec x). then find the value of x.
The general solution of x(1 + y2)1/2 dx + y(1 + x2)1/2 dy = 0 is ______.
The number of principal solutions of tan 2θ = 1 is ______.
The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.
The general solution to cos100x – sin100x = 1 is ______.
The general solution of cot 4x = –1 is ______.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
