Advertisements
Advertisements
प्रश्न
Find the principal value of the following:
tan−1 (−1)
Advertisements
उत्तर
Let tan−1 (−1) = y
Then tan y = −1 = `-tan (pi/2) = tan (-pi/2)`
We know that the range of the principal value branch of tan−1 is `(-pi/2, pi/2)` and `tan(-pi/4) = - 1`.
Where `-pi/4 ∈ (-pi/2, pi/2)`
Therefore, the principal value of tan−1 (−1) is `pi/4`.
APPEARS IN
संबंधित प्रश्न
Find the value of the following:
`tan^(-1)(1) + cos^(-1) (-1/2) + sin^(-1) (-1/2)`
If sin−1 x = y, then ______.
Find the principal value of `sin^-1(1/sqrt2)`
`sin^-1{cos(sin^-1 sqrt3/2)}`
Find the domain of the following function:
`f(x)=sin^-1x^2`
If `sin^-1 x + sin^-1 y+sin^-1 z+sin^-1 t=2pi` , then find the value of x2 + y2 + z2 + t2
Solve for x:
`tan^-1 [(x-1),(x-2)] + tan^-1 [(x+1),(x+2)] = x/4`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of sinA.
Find the principal value of the following: tan-1(– 1)
Find the principal solutions of the following equation:
sin 2θ = `− 1/(sqrt2)`
Find the principal solutions of the following equation:
tan 5θ = -1
Evaluate cot(tan−1(2x) + cot−1(2x))
Prove that `2 tan^-1 (3/4) = tan^-1(24/7)`
Find the value of `cos^-1 (1/2) + tan^-1 (1/sqrt(3))`
Find the principal value of the following:
`sin^-1 (- 1/2)`
Evaluate: sin`[1/2 cos^-1 (4/5)]`
Find the principal value of `sec^-1 (- sqrt(2))`
If `sin^-1x + cos^-1y = (3pi)/10,` then `cos^-1x + sin^-1y =` ______
If `3sin^-1((2x)/(1 + x^2)) - 4cos^-1((1 - x^2)/(1 + x^2)) + 2tan^-1((2x)/(1 - x^2)) = pi/3`, then x is equal to ______
`sin{tan^-1((1 - x^2)/(2x)) + cos^-1((1 - x^2)/(1 + x^2))}` is equal to ______
`cos^-1 4/5 + tan^-1 3/5` = ______.
Prove that `cot(pi/4 - 2cot^-1 3)` = 7
Show that `2tan^-1 (-3) = (-pi)/2 + tan^-1 ((-4)/3)`
Show that `sin^-1 5/13 + cos^-1 3/5 = tan^-1 63/16`
If `"x + y" = "x"/4` then (1+ tanx)(1 + tany) is equal to ____________.
If tan-1 (x – 1) + tan-1 x + tan-1 (x + 1) = tan-1 3x, then the values of x are ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
`sin[π/3 - sin^-1 (-1/2)]` is equal to:
The inverse of `f(x) = sqrt(3x^2 - 4x + 5)` is
`tan^-1 (1 - x)/(1 + x) = 1/2tan^-1x, (x > 0)`, x then will be equal to.
cos–1(cos10) is equal to ______.
Number of values of x which lie in [0, 2π] and satisfy the equation
`(cos x/4 - 2sinx) sinx + (1 + sin x/4 - 2cosx)cosx` = 0
If ax + b (sec (tan–1 x)) = c and ay + b (sec.(tan–1 y)) = c, then `(x + y)/(1 - xy)` = ______.
sin [cot–1 (cos (tan–1 x))] = ______.
Find the value of `cos(x/2)`, if tan x = `5/12` and x lies in third quadrant.
The value of `tan(cos^-1 4/5 + tan^-1 2/3)` is ______.
Find the value of `sin(2cos^-1 sqrt(5)/3)`.
Find the value of `tan^-1(x/y) + tan^-1((y - x)/(y + x))`
