Advertisements
Advertisements
Question
Evaluate tan (tan–1(– 4)).
Solution
Since tan (tan–1x) = x, ∀ x ∈ R, tan (tan–1(– 4)
= – 4.
APPEARS IN
RELATED QUESTIONS
If `sin (sin^(−1)(1/5)+cos^(−1) x)=1`, then find the value of x.
Prove that `2tan^(-1)(1/5)+sec^(-1)((5sqrt2)/7)+2tan^(-1)(1/8)=pi/4`
Solve for x : tan-1 (x - 1) + tan-1x + tan-1 (x + 1) = tan-1 3x
Prove the following:
`3cos^(-1) x = cos^(-1)(4x^3 - 3x), x in [1/2, 1]`
Write the function in the simplest form: `tan^(-1) ((cos x - sin x)/(cos x + sin x)) `,` 0 < x < pi`
Find the value of the following:
`tan^-1 [2 cos (2 sin^-1 1/2)]`
Prove that:
`cot^(-1) ((sqrt(1+sin x) + sqrt(1-sinx))/(sqrt(1+sin x) - sqrt(1- sinx))) = x/2`, `x in (0, pi/4)`
Prove `(9pi)/8 - 9/4 sin^(-1) 1/3 = 9/4 sin^(-1) (2sqrt2)/3`
Solve for x : \[\tan^{- 1} \left( \frac{x - 2}{x - 1} \right) + \tan^{- 1} \left( \frac{x + 2}{x + 1} \right) = \frac{\pi}{4}\] .
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 (cos pi)`
Find the value of the expression in terms of x, with the help of a reference triangle
`tan(sin^-1(x + 1/2))`
Simplify: `tan^-1 x/y - tan^-1 (x - y)/(x + y)`
Solve: `2tan^-1 (cos x) = tan^-1 (2"cosec" x)`
Choose the correct alternative:
If `sin^-1x + sin^-1y = (2pi)/3` ; then `cos^-1x + cos^-1y` is equal to
Choose the correct alternative:
The equation tan–1x – cot–1x = `tan^-1 (1/sqrt(3))` has
Choose the correct alternative:
sin(tan–1x), |x| < 1 is equal to
Evaluate `cos[sin^-1 1/4 + sec^-1 4/3]`
Prove that cot–17 + cot–18 + cot–118 = cot–13
If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is ______.
If `sin^-1 ((2"a")/(1 + "a"^2)) + cos^-1 ((1 - "a"^2)/(1 + "a"^2)) = tan^-1 ((2x)/(1 - x^2))`. where a, x ∈ ] 0, 1, then the value of x is ______.
If `"tan"^-1 ("cot" theta) = 2theta, "then" theta` is equal to ____________.
`"sin" {2 "cos"^-1 ((-3)/5)}` is equal to ____________.
If tan-1 2x + tan-1 3x = `pi/4,` then x is ____________.
`"cos"^-1["cos"(2"cot"^-1(sqrt2 - 1))]` = ____________.
`"cos"^-1 1/2 + 2 "sin"^-1 1/2` is equal to ____________.
`"cos"^-1 (1/2)`
The Simplest form of `cot^-1 (1/sqrt(x^2 - 1))`, |x| > 1 is
`"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`
