Advertisements
Advertisements
प्रश्न
Find the value of the following:
`tan^(-1) (tan (7pi)/6)`
Advertisements
उत्तर
`tan^(-1) (tan (7pi)/6) ≠ (7pi)/6` as the range of the principal value branch of tan−1 is `(-pi/2, pi/2)`.
So, `tan^(-1) (tan (7pi)/6)`
= `tan^-1(tan(pi + pi/6))`
= `tan^-1(tan pi/6)`
= `pi/6`
APPEARS IN
संबंधित प्रश्न
Find the principal value of the following:
`cos^(-1) (sqrt3/2)`
Find the principal value of the following:
`sec^(-1) (2/sqrt(3))`
Find the principal value of the following:
`cot^(-1) (sqrt3)`
Find the value of the following:
`tan^(-1)(1) + cos^(-1) (-1/2) + sin^(-1) (-1/2)`
If `sin^-1 x + sin^-1 y+sin^-1 z+sin^-1 t=2pi` , then find the value of x2 + y2 + z2 + t2
Evaluate the following:
`cot^-1 1/sqrt3-\text(cosec)^-1(-2)+sec^-1(2/sqrt3)`
Evaluate the following:
`\text(cosec)^-1(-2/sqrt3)+2cot^-1(-1)`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of tan `A/2`
Find the principal value of the following: tan- 1( - √3)
Prove the following:
`tan^-1[sqrt((1 - cosθ)/(1 + cosθ))] = θ/(2)`, if θ ∈ (– π, π).
Find the principal solutions of the following equation:
tan 5θ = -1
Find the principal solutions of the following equation:
cot 2θ = 0.
The principal value of sin−1`(1/2)` is ______
If `sin(sin^-1(1/5) + cos^-1(x))` = 1, then x = ______
Evaluate cot(tan−1(2x) + cot−1(2x))
Find the principal value of `cos^-1 sqrt(3)/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 ______
The domain of the function y = sin–1 (– x2) is ______.
The domain of the function defined by f(x) = sin–1x + cosx is ______.
The equation tan–1x – cot–1x = `(1/sqrt(3))` has ______.
If 2 tan–1(cos θ) = tan–1(2 cosec θ), then show that θ = π 4, where n is any integer.
All trigonometric functions have inverse over their respective domains.
If tan-1 (x – 1) + tan-1 x + tan-1 (x + 1) = tan-1 3x, then the values of x are ____________.
If 6sin-1 (x2 – 6x + 8.5) = `pi`, then x is equal to ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
The range of sin-1 x + cos-1 x + tan-1 x is ____________.
If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt "cos" alpha) = "x",` then sinx is equal to ____________.
`"cos"^-1 ("cos" ((7pi)/6))` is equal to ____________.
The equation of the tangent to the curve given by x = a sin3t, y = bcos3t at a point where t = `pi/2` is
If A = `[(cosx, sinx),(-sinx, cosx)]`, then A1 A–1 is
What is the principal value of cosec–1(2).
`tan^-1 (1 - x)/(1 + x) = 1/2tan^-1x, (x > 0)`, x then will be equal to.
Consider f(x) = sin–1[2x] + cos–1([x] – 1) (where [.] denotes greatest integer function.) If domain of f(x) is [a, b) and the range of f(x) is {c, d} then `a + b + (2d)/c` is equal to ______. (where c < d)
`cot^-1(sqrt(cos α)) - tan^-1 (sqrt(cos α))` = x, then sin x = ______.
