Advertisements
Advertisements
प्रश्न
Prove that `2 tan^-1 (3/4) = tan^-1(24/7)`
उत्तर
`2 tan^-1 (3/4)`
= `tan^-1 (3/4) + tan^-1 (3/4)`
= `tan^-1 ((3/4 + 3/4)/(1 - 3/4 xx 3/4))` .......`[tan^-1"a" + tan^-1"b" = tan^-1(("a" + "b")/(1 - "ab"))]`
= `tan^-1 ((6/4)/(7/16))`
= `tan^-1 (24/7)`
APPEARS IN
संबंधित प्रश्न
Find the principal value of tan−1 (−1)
Find the value of the following:
`cos^(-1) (cos (13pi)/6)`
Find the value of the following:
`tan^(-1) (tan (7x)/6)`
Prove that:
`tan^-1 ((sqrt(1 + x) - sqrt(1 - x))/(sqrt(1 + x) + sqrt(1 - x))) = pi/4 - 1/2 cos^-1 x`, for `- 1/sqrt2 <= x <= 1`
[Hint: put x = cos 2θ]
`sin^-1 1/2-2sin^-1 1/sqrt2`
Find the domain of the following function:
`f(x)=sin^-1x^2`
Find the domain of the following function:
`f(x)sin^-1sqrt(x^2-1)`
Evaluate the following:
`tan^-1(tan (5pi)/6)+cos^-1{cos((13pi)/6)}`
Find the domain of `f(x)=cotx+cot^-1x`
Evaluate the following:
`cot^-1 1/sqrt3-\text(cosec)^-1(-2)+sec^-1(2/sqrt3)`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of sinA
In ΔABC prove that `(b + c - a) tan "A"/(2) = (c + a - b)tan "B"/(2) = (a + b - c)tan "C"/(2)`.
In ΔABC prove that `sin "A"/(2). sin "B"/(2). sin "C"/(2) = ["A(ΔABC)"]^2/"abcs"`
Find the principal value of the following: `sin^-1 (1/2)`
Find the principal value of the following: tan-1(– 1)
Find the principal value of the following: cos- 1`(-1/2)`
Evaluate the following:
`tan^-1(1) + cos^-1(1/2) + sin^-1(1/2)`
Evaluate the following:
`tan^-1 sqrt(3) - sec^-1 (-2)`
Evaluate the following:
`"cosec"^-1(-sqrt(2)) + cot^-1(sqrt(3))`
Prove the following:
`sin^-1(1/sqrt(2)) -3sin^-1(sqrt(3)/2) = -(3π)/(4)`
Prove the following:
`sin^-1(3/5) + cos^-1(12/13) = sin^-1(56/65)`
Prove the following:
`2tan^-1(1/3) = tan^-1(3/4)`
Prove the following:
`tan^-1["cosθ + sinθ"/"cosθ - sinθ"] = pi/(4) + θ, if θ ∈ (- pi/4, pi/4)`
The principal value of sin−1`(1/2)` is ______
The principal value of cos−1`(-1/2)` is ______
Evaluate:
`sin[cos^-1 (3/5)]`
Find the value of `cos^-1 (1/2) + tan^-1 (1/sqrt(3))`
Evaluate `cos[pi/6 + cos^-1 (- sqrt(3)/2)]`
Prove that cot−1(7) + 2 cot−1(3) = `pi/4`
Find the principal value of the following:
`sin^-1 (- 1/2)`
Find the principal value of the following:
tan-1 (-1)
Find the principal value of the following:
`sec^-1 (-sqrt2)`
Prove that:
2 tan-1 (x) = `sin^-1 ((2x)/(1 + x^2))`
Express `tan^-1 ((cos x - sin x)/(cos x + sin x))`, 0 < x < π in the simplest form.
Find the principal value of cosec–1(– 1)
Find the principal value of `sec^-1 (- sqrt(2))`
A man standing directly opposite to one side of a road of width x meter views a circular shaped traffic green signal of diameter ‘a’ meter on the other side of the road. The bottom of the green signal Is ‘b’ meter height from the horizontal level of viewer’s eye. If ‘a’ denotes the angle subtended by the diameter of the green signal at the viewer’s eye, then prove that α = `tan^-1 (("a" + "b")/x) - tan^-1 ("b"/x)`
In ΔABC, tan`A/2 = 5/6` and tan`C/2 = 2/5`, then ______
The principle solutions of equation tan θ = -1 are ______
In Δ ABC, with the usual notations, if sin B sin C = `"bc"/"a"^2`, then the triangle is ______.
Which of the following function has period 2?
The value of 2 `cot^-1 1/2 - cot^-1 4/3` is ______
`sin^2(sin^-1 1/2) + tan^2 (sec^-1 2) + cot^2(cosec^-1 4)` = ______.
`tan[2tan^-1 (1/3) - pi/4]` = ______.
`cos(2sin^-1 3/4+cos^-1 3/4)=` ______.
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^-1(-1/2) + tan^-1(-1/sqrt(3)))/(sec^-1 (-2/sqrt(3)) + cos^-1(1/sqrt(2))` = ______.
If `3tan^-1x +cot^-1x = pi`, then xis equal to ______.
The value of `sin^-1[cos(pi/3)] + sin^-1[tan((5pi)/4)]` is ______.
The domain of the function defined by f(x) = sin–1x + cosx is ______.
The equation tan–1x – cot–1x = `(1/sqrt(3))` has ______.
Show that `2tan^-1 (-3) = (-pi)/2 + tan^-1 ((-4)/3)`
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.
When `"x" = "x"/2`, then tan x is ____________.
`"sin" 265° - "cos" 265°` is ____________.
If `"cos"^-1 "x + sin"^-1 "x" = pi`, then the value of x is ____________.
If 6sin-1 (x2 – 6x + 8.5) = `pi`, then x is equal to ____________.
`"sin" ["cot"^-1 {"cos" ("tan"^-1 "x")}] =` ____________.
Find the value of sec2 (tan-1 2) + cosec2 (cot-1 3) ____________.
`2"tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
If |Z1| = |Z2| and arg (Z1) + arg (Z2) = 0, then
If `(-1)/sqrt(2) ≤ x ≤ 1/sqrt(2)` then `sin^-1 (2xsqrt(1 - x^2))` is equal to
`tan^-1 (1 - x)/(1 + x) = 1/2tan^-1x, (x > 0)`, x then will be equal to.
`2tan^-1 (cos x) = tan^-1 (2"cosec" x)`, then 'x' will be equal to
If `sin(sin^-1 1/5 + cos^-1 x) = 1`, the what will be the value of x?
If f(x) = x5 + 2x – 3, then (f–1)1 (–3) = ______.
cos–1(cos10) is equal to ______.
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.
Find the value of `tan^-1(x/y) + tan^-1((y - x)/(y + x))`
