Advertisements
Advertisements
प्रश्न
Find the value of the following:
`tan^(-1)(1) + cos^(-1) (-1/2) + sin^(-1) (-1/2)`
उत्तर १
Let `tan^(-1) (1)` = x Then tan x= 1 = tan `pi/4`
`:. tan^(-1) (1) = pi/4`
Let `cos^(-1) (-1/2) = y` Then, `cos y = -1/2 = -cos(pi/3) = cos(pi - pi/3) = cos ((2pi)/3)`
`:. cos^(-1) (- 1/2) = (2pi)/3`
Let `sin^(-1) (-1/2) = z`. Then `sin z =-1/2 = -sin(pi/6) = sin(-pi/6)`
`:. sin^(-1)(-1/2) = - pi/6`
`:. tan^(-1) (1) + cos^(-1) (-1/2) + sin^(-1) (-1/2)`
`= pi/4 + (2pi)/3 - pi/6`
`= (3pi + 8pi - 2pi)/12 `
`= (9pi)/12 = (3pi)/4`
उत्तर २
`"tan"^-1 (1) + "cos"^-1 (-1/2) + "sin"^-1 (-1/2)`
`= "tan"^-1 ("tan" pi/4) + "cos"^-1 ("cos" (2pi)/3) + "sin"^-1 "sin" ((-pi)/6)`
`= pi/4 + (2pi)/3 + ((-pi)/6)`
`= (3pi + 8pi - 2pi)/12`
`= (9 pi)/12 = (3 pi)/4`
APPEARS IN
संबंधित प्रश्न
If `sin^-1(1-x) -2sin^-1x = pi/2` then x is
- -1/2
- 1
- 0
- 1/2
If `tan^-1((x-1)/(x-2))+cot^-1((x+2)/(x+1))=pi/4; `
Find the principal values of `sin^(-1) (-1/2)`
Find the principal value of `cot^(-1) (sqrt3)`
Find the principal value of `cos^(-1) (-1/sqrt2)`
Find the value of the following:
If sin−1 x = y, then
`sin^-1{cos(sin^-1 sqrt3/2)}`
Find the domain of the following function:
`f(x)sin^-1sqrt(x^2-1)`
Evaluate the following:
`tan^-1 1+cos^-1 (-1/2)+sin^-1(-1/2)`
Find the set of values of `cosec^-1(sqrt3/2)`
Evaluate the following:
`tan^-1(-1/sqrt3)+cot^-1(1/sqrt3)+tan^-1(sin(-pi/2))`
Evaluate: tan `[ 2 tan^-1 (1)/(2) – cot^-1 3]`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of cosA
In ΔABC prove that `sin "A"/(2). sin "B"/(2). sin "C"/(2) = ["A(ΔABC)"]^2/"abcs"`
Find the principal value of the following: tan- 1( - √3)
Find the principal value of the following: sin-1 `(1/sqrt(2))`
Evaluate the following:
`"cosec"^-1(-sqrt(2)) + cot^-1(sqrt(3))`
Find the principal solutions of the following equation:
sin 2θ = `− 1/(sqrt2)`
Evaluate:
`sin[cos^-1 (3/5)]`
Express `tan^-1 [(cos x)/(1 - sin x)], - pi/2 < x < (3pi)/2` in the simplest form.
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)` = ______.
The principal value of `sin^-1 (sin (3pi)/4)` is ______.
The domain of y = cos–1(x2 – 4) is ______.
If 2 tan–1(cos θ) = tan–1(2 cosec θ), then show that θ = π 4, where n is any integer.
Solve the following equation `cos(tan^-1x) = sin(cot^-1 3/4)`
Show that `sin^-1 5/13 + cos^-1 3/5 = tan^-1 63/16`
`"cos" 2 theta` is not equal to ____________.
If `"sin"^-1("x"^2 - 7"x" + 12) = "n"pi, AA "n" in "I"`, then x = ____________.
`"cos"^-1 1/2 + 2 "sin"^-1 1/2` 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 ____________.
Find the value of sec2 (tan-1 2) + cosec2 (cot-1 3) ____________.
If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt "cos" alpha) = "x",` then sinx is equal to ____________.
Which of the following functions is inverse of itself?
Domain and Rariges of cos–1 is:-
What will be the principal value of `sin^-1(-1/2)`?
Value of `sin(pi/3 - sin^1 (- 1/2))` is 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)
If tan 4θ = `tan(2/θ)`, then the general value of θ is ______.
