Advertisements
Advertisements
Question
Find the value of `cot(tan^(-1) a + cot^(-1) a)`
Solution
`cot(tan^(-1) a + cos^(-1))`
`= cot(pi/2) [tan^(-1) x + cot^(-1) x = pi/2]`
= 0
APPEARS IN
RELATED QUESTIONS
If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.
Prove the following:
`3cos^(-1) x = cos^(-1)(4x^3 - 3x), x in [1/2, 1]`
Prove `tan^(-1) 2/11 + tan^(-1) 7/24 = tan^(-1) 1/2`
Write the following function in the simplest form:
`tan^(-1) (sqrt(1+x^2) -1)/x, x != 0`
Write the following function in the simplest form:
`tan^(-1) (sqrt((1-cos x)/(1 + cos x))), x < pi`
Find the value of the following:
`tan^-1 [2 cos (2 sin^-1 1/2)]`
Find the value of the given expression.
`tan^(-1) (tan (3pi)/4)`
`cos^(-1) (cos (7pi)/6)` is equal to ______.
Prove that:
`cos^(-1) 4/5 + cos^(-1) 12/13 = cos^(-1) 33/65`
Prove that:
`cos^(-1) 12/13 + sin^(-1) 3/5 = sin^(-1) 56/65`
Prove `(9pi)/8 - 9/4 sin^(-1) 1/3 = 9/4 sin^(-1) (2sqrt2)/3`
sin–1 (1 – x) – 2 sin–1 x = `pi/2` , then x is equal to ______.
Prove that `tan {pi/4 + 1/2 cos^(-1) a/b} + tan {pi/4 - 1/2 cos^(-1) a/b} = (2b)/a`
If y = `(x sin^-1 x)/sqrt(1 -x^2)`, prove that: `(1 - x^2)dy/dx = x + y/x`
Find: ∫ sin x · log cos x dx
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 [sin 5]`
Find the value of `cot[sin^-1 3/5 + sin^-1 4/5]`
Prove that `tan^-1 2/11 + tan^-1 7/24 = tan^-1 1/2`
Solve: `sin^-1 5/x + sin^-1 12/x = pi/2`
Choose the correct alternative:
`sin^-1 (tan pi/4) - sin^-1 (sqrt(3/x)) = pi/6`. Then x is a root of the equation
Choose the correct alternative:
If `cot^-1(sqrt(sin alpha)) + tan^-1(sqrt(sin alpha))` = u, then cos 2u is equal to
Evaluate tan (tan–1(– 4)).
Prove that `tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/((1 + x^2) - sqrt(1 - x^2))) = pi/2 + 1/2 cos^-1x^2`
If |x| ≤ 1, then `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` is equal to ______.
The number of real solutions of the equation `sqrt(1 + cos 2x) = sqrt(2) cos^-1 (cos x)` in `[pi/2, pi]` is ______.
The maximum value of sinx + cosx is ____________.
The value of `"tan"^-1 (1/2) + "tan"^-1 (1/3) + "tan"^-1 (7/8)` is ____________.
`"cot" (pi/4 - 2 "cot"^-1 3) =` ____________.
The value of expression 2 `"sec"^-1 2 + "sin"^-1 (1/2)`
sin (tan−1 x), where |x| < 1, is equal to:
`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 + "tan"^-1 1/8 =` ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
If `6"sin"^-1 ("x"^2 - 6"x" + 8.5) = pi,` then x is equal to ____________.
`"sin"^-1 (1/sqrt2)`
If `3 "sin"^-1 ((2"x")/(1 + "x"^2)) - 4 "cos"^-1 ((1 - "x"^2)/(1 + "x"^2)) + 2 "tan"^-1 ((2"x")/(1 - "x"^2)) = pi/3` then x is equal to ____________.
If `cos^-1(2/(3x)) + cos^-1(3/(4x)) = π/2(x > 3/4)`, then x is equal to ______.
If `tan^-1 ((x - 1)/(x + 1)) + tan^-1 ((2x - 1)/(2x + 1)) = tan^-1 (23/36)` = then prove that 24x2 – 23x – 12 = 0
`"tan" ^-1 sqrt3 - "cot"^-1 (- sqrt3)` is equal to ______.
Solve for x: `sin^-1(x/2) + cos^-1x = π/6`
If sin–1x + sin–1y + sin–1z = π, show that `x^2 - y^2 - z^2 + 2yzsqrt(1 - x^2) = 0`
