Advertisements
Advertisements
Question
Choose the correct alternative:
The equation tan–1x – cot–1x = `tan^-1 (1/sqrt(3))` has
Options
no solution
unique solution
two solutions
infinite number of solutions
Solution
unique solution
APPEARS IN
RELATED QUESTIONS
Prove the following:
`3sin^(-1) x = sin^(-1)(3x - 4x^3), x in [-1/2, 1/2]`
Write the function in the simplest form: `tan^(-1) ((cos x - sin x)/(cos x + sin x)) `,` 0 < x < pi`
Write the following function in the simplest form:
`tan^(-1) ((3a^2 x - x^3)/(a^3 - 3ax^2)), a > 0; (-a)/sqrt3 <= x a/sqrt3`
Find the value of `cot(tan^(-1) a + cot^(-1) a)`
Find the value of the given expression.
`tan^(-1) (tan (3pi)/4)`
Solve for x : \[\cos \left( \tan^{- 1} x \right) = \sin \left( \cot^{- 1} \frac{3}{4} \right)\] .
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]`
If tan–1x + tan–1y + tan–1z = π, show that x + y + z = xyz
Choose the correct alternative:
sin–1(2 cos2x – 1) + cos–1(1 – 2 sin2x) =
Prove that cot–17 + cot–18 + cot–118 = cot–13
Show that `2tan^-1 {tan alpha/2 * tan(pi/4 - beta/2)} = tan^-1 (sin alpha cos beta)/(cosalpha + sinbeta)`
Show that `tan(1/2 sin^-1 3/4) = (4 - sqrt(7))/3` and justify why the other value `(4 + sqrt(7))/3` is ignored?
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 cos–1α + cos–1β + cos–1γ = 3π, then α(β + γ) + β(γ + α) + γ(α + β) equals ______.
The value of expression 2 `"sec"^-1 2 + "sin"^-1 (1/2)`
If `"sin"^-1 (1 - "x") - 2 "sin"^-1 ("x") = pi/2,` then x is equal to ____________.
Find the value of `sin^-1 [sin((13π)/7)]`
If `cos^-1(2/(3x)) + cos^-1(3/(4x)) = π/2(x > 3/4)`, then x is equal to ______.
