Advertisements
Advertisements
Question
Find the value of the given expression.
`tan^(-1) (tan (3pi)/4)`
Advertisements
Solution
We know that tan−1 (tan x) = x if `x ∈ (-pi/2, pi/2)` which is the principal value branch of tan−1 x.
Here `(3pi)/4 ∉ ((-pi)/2, pi/2)`
Now, `tan^(-1) (tan (3pi)/4)` can be written as
`tan^(-1) (tan (3pi)/4)`
= `tan^(-1) [-tan ((-3pi)/4)]`
= `tan^(-1) [-tan(pi - pi/4)]`
= `tan^(-1) [-tan pi/4]`
= `tan^(-1) [tan(-pi/4)]` where `- pi/4 ∈ ((-pi)/2, pi/2)`
∴ `tan^(-1) (tan (3pi)/4)`
= `tan^(-1) [tan((-pi)/4)]`
= `(-pi)/4`
APPEARS IN
RELATED QUESTIONS
If `sin (sin^(−1)(1/5)+cos^(−1) x)=1`, then find the value of x.
Prove the following:
3 sin−1 x = sin−1 (3x − 4x3), `x ∈ [-1/2, 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)))`, 0 < x < π
Find the value of `cot(tan^(-1) a + cot^(-1) a)`
Find the value of the given expression.
`sin^(-1) (sin (2pi)/3)`
Find the value of the given expression.
`tan(sin^(-1) 3/5 + cot^(-1) 3/2)`
Prove that:
`sin^(-1) 8/17 + sin^(-1) 3/5 = tan^(-1) 77/36`
Prove that:
`tan^(-1) 63/16 = sin^(-1) 5/13 + cos^(-1) 3/5`
Solve `tan^(-1) - tan^(-1) (x - y)/(x+y)` is equal to
(A) `pi/2`
(B). `pi/3`
(C) `pi/4`
(D) `(-3pi)/4`
Solve the following equation for x: `cos (tan^(-1) x) = sin (cot^(-1) 3/4)`
Prove that `3sin^(-1)x = sin^(-1) (3x - 4x^3)`, `x in [-1/2, 1/2]`
If tan-1 x - cot-1 x = tan-1 `(1/sqrt(3)),`x> 0 then find the value of x and hence find the value of sec-1 `(2/x)`.
Solve for x : `tan^-1 ((2-"x")/(2+"x")) = (1)/(2)tan^-1 ("x")/(2), "x">0.`
Find the value of `sin^-1[cos(sin^-1 (sqrt(3)/2))]`
Prove that `tan^-1 2/11 + tan^-1 7/24 = tan^-1 1/2`
Solve: `cot^-1 x - cot^-1 (x + 2) = pi/12, x > 0`
Find the number of solutions of the equation `tan^-1 (x - 1) + tan^-1x + tan^-1(x + 1) = tan^-1(3x)`
Choose the correct alternative:
sin(tan–1x), |x| < 1 is equal to
Evaluate `tan^-1(sin((-pi)/2))`.
Evaluate: `sin^-1 [cos(sin^-1 sqrt(3)/2)]`
Evaluate `cos[cos^-1 ((-sqrt(3))/2) + pi/6]`
Prove that `sin^-1 8/17 + sin^-1 3/5 = sin^-1 7/85`
If a1, a2, a3,...,an is an arithmetic progression with common difference d, then evaluate the following expression.
`tan[tan^-1("d"/(1 + "a"_1 "a"_2)) + tan^-1("d"/(21 + "a"_2 "a"_3)) + tan^-1("d"/(1 + "a"_3 "a"_4)) + ... + tan^-1("d"/(1 + "a"_("n" - 1) "a""n"))]`
The minimum value of sinx - cosx is ____________.
The value of cot `("cosec"^-1 5/3 + "tan"^-1 2/3)` is ____________.
`"sin" {2 "cos"^-1 ((-3)/5)}` is equal to ____________.
The value of sin (2tan-1 (0.75)) is equal to ____________.
If `"tan"^-1 (("x" - 1)/("x" + 2)) + "tan"^-1 (("x" + 1)/("x" + 2)) = pi/4,` then x is equal to ____________.
The value of cot-1 9 + cosec-1 `(sqrt41/4)` is given by ____________.
`"tan" (pi/4 + 1/2 "cos"^-1 "x") + "tan" (pi/4 - 1/2 "cos"^-1 "x") =` ____________.
`"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`
`"cos"^-1 (1/2)`
If `"sin" {"sin"^-1 (1/2) + "cos"^-1 "x"} = 1`, then the value of x is ____________.
If `"sin"^-1 (1 - "x") - 2 "sin"^-1 ("x") = pi/2,` then x is equal to ____________.
What is the value of cos (sec–1x + cosec–1x), |x| ≥ 1
Write the following function in the simplest form:
`tan^-1 ((cos x - sin x)/(cos x + sin x)), (-pi)/4 < x < (3 pi)/4`
