Advertisements
Advertisements
Question
Show that `tan^-1 1/2 - tan^-1 1/4 = tan^-1 2/9`.
Advertisements
Solution
LHS = `tan^-1 1/2 - tan^-1 1/4`
`= tan^-1 [(1/2 - 1/4)/(1 + (1/2)(1/4))]`
`= tan^-1 ((4 - 2)/(8 + 1))`
`= tan^-1 (2/9)` = RHS.
APPEARS IN
RELATED QUESTIONS
Find the principal solution of the following equation:
sin θ = `-1/2`
Find the general solution of the following equation:
cot θ = 0.
Find the general solution of the following equation:
sec θ = `sqrt(2)`.
Find the general solution of the following equation:
sin 2θ = `1/2`
Find the general solution of the following equation:
tan `(2θ)/(3) = sqrt3`
Find the general solution of the following equation:
sin θ = tan θ
With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c2 .
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 = ____.
Select the correct option from the given alternatives:
In ΔABC, ac cos B - bc cos A = _______
Select the correct option from the given alternatives:
`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______
Select the correct option from the given alternatives:
In any ΔABC, if acos B = bcos A, then the triangle is
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`
Find the general solutions of the following equation:
sin2 θ - cos2 θ = 1
Find the general solutions of the following equation:
sin θ - cos θ = 1
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))`
The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______
If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1
`cos^-1 (cos (4pi)/3)` = ______.
`int 1/(sin x * cos x)` dx = ?
If `|bar"a"|` = 10, `|bar"b"| = 2`, then `sqrt(|bar"a" xx bar"b"|^2 + |bar"a"*bar"b"|^2)` = ?
If tan-1 x + 2cot-1 x = `(5pi)/6`, then x is
If f(x) = sin-1`(sqrt((1 - x)/2))`, then f'(x) = ?
If x + y = `pi/2`, then the maximum value of sin x. sin y is.
The principal solutions of cot x = `sqrt3` are ______.
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 value of `tan^-1 1/3 + tan^-1 1/5 + tan^-1 1/7 + tan^-1 1/8` is ______.
The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 is ______
The general solution of 4sin2 x = 1 is ______.
The general solution of cosec x = `-sqrt2` is ______
Find the principal solutions of cot θ = 0
The general solution of x(1 + y2)1/2 dx + y(1 + x2)1/2 dy = 0 is ______.
Which of the following equation has no solution?
The number of principal solutions of tan 2θ = 1 is ______.
Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.
The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is ______.
With usual notations, in any ΔABC, if a cos B = b cos A, then the triangle is ______.
The general solution to cos100x – sin100x = 1 is ______.
If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.
