Advertisements
Advertisements
प्रश्न
Find the principal value of the following: cos- 1`(-1/2)`
उत्तर
The principal value branch of cos- 1x [0, π].
Let cos- 1`(-1/2)`= α, where 0 ≤ α ≤ π
∴ cos α = `-1/2 = -cos pi/(3)`
∴ cos α = `cos(pi - pi/3)` ...[∵ cos(π – θ) = – cosθ]
∴ cos α = cos `(2pi)/(3)`
∴ α = `(2pi)/(3) ...[∵ 0 ≤ (2pi)/(3) ≤ pi]`
∴ the principal value of cos- 1`(-1/2) "is" (2pi)/(3)`.
APPEARS IN
संबंधित प्रश्न
If `tan^-1((x-1)/(x-2))+cot^-1((x+2)/(x+1))=pi/4; `
Show that `2sin^-1(3/5) = tan^-1(24/7)`
Find the principal value of cosec−1 (2)
Find the principal value of `cos^(-1) (-1/2)`
Find the principal value of tan−1 (−1)
Find the principal value of `sec^(-1) (2/sqrt(3))`
Find the principal value of `cos^(-1) (-1/sqrt2)`
Find the value of the following:
If sin−1 x = y, then
`tan^(-1) sqrt3 - sec^(-1)(-2)` is equal to ______.
`sin^-1{cos(sin^-1 sqrt3/2)}`
Find the domain of the following function:
`f(x) = sin^-1x + sinx`
Evaluate the following:
`tan^-1(tan (5pi)/6)+cos^-1{cos((13pi)/6)}`
Evaluate the following:
`\text(cosec)^-1(-2/sqrt3)+2cot^-1(-1)`
In ΔABC prove that `sin "A"/(2). sin "B"/(2). sin "C"/(2) = ["A(ΔABC)"]^2/"abcs"`
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(-1/2) + cos^-1(-sqrt(3)/2) = cos^-1(-1/2)`
Prove the following:
`tan^-1(1/2) + tan^-1(1/3) = pi/(4)`
Find the principal solutions of the following equation:
cot 2θ = 0.
Prove that `2 tan^-1 (3/4) = tan^-1(24/7)`
Show that `sin^-1(3/5) + sin^-1(8/17) = cos^-1(36/85)`
Find the principal value of the following:
`sec^-1 (-sqrt2)`
Evaluate:
`cos[tan^-1 (3/4)]`
Show that `sin^-1 (- 3/5) - sin^-1 (- 8/17) = cos^-1 (84/85)`
Express `tan^-1 [(cos x)/(1 - sin x)], - pi/2 < x < (3pi)/2` in the simplest form.
Find the principal value of `sec^-1 (- sqrt(2))`
If `sin^-1(x/13) + cosec^-1(13/12) = pi/2`, then the value of x is ______
In Δ ABC, with the usual notations, if sin B sin C = `"bc"/"a"^2`, then the triangle is ______.
sin[3 sin-1 (0.4)] = ______.
If `sin^-1x + cos^-1y = (3pi)/10,` then `cos^-1x + sin^-1y =` ______
`sin^2(sin^-1 1/2) + tan^2 (sec^-1 2) + cot^2(cosec^-1 4)` = ______.
If 2tan-1 (cos x) = tan-1 (cosec2 x), then x = ______.
The principal value of `sin^-1 (sin (3pi)/4)` is ______.
`tan[2tan^-1 (1/3) - pi/4]` = ______.
In a triangle ABC, ∠C = 90°, then the value of `tan^-1 ("a"/("b + c")) + tan^-1("b"/("c + a"))` is ______.
`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{tan^-1((1 - x^2)/(2x)) + cos^-1((1 - x^2)/(1 + x^2))}` is equal to ______
`cos^-1 4/5 + tan^-1 3/5` = ______.
The value of `sin^-1[cos(pi/3)] + sin^-1[tan((5pi)/4)]` is ______.
The domain of y = cos–1(x2 – 4) is ______.
Prove that `tan^-1 1/4 + tan^-1 2/9 = sin^-1 1/sqrt(5)`
`"sin"^2 25° + "sin"^2 65°` is equal to ____________.
If `"x + y" = "x"/4` then (1+ tanx)(1 + tany) is equal to ____________.
If sin-1 x – cos-1 x `= pi/6,` then x = ____________.
`"sin"^-1 (1/sqrt2)`
`2 "tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
The value of `"cos"^-1 ("cos" ((33 pi)/5))` is ____________.
`"cos"^-1 ["cos" (2 "cot"^-1 (sqrt2 - 1))] =` ____________.
Find the value of sec2 (tan-1 2) + cosec2 (cot-1 3) ____________.
`sin[π/3 - sin^-1 (-1/2)]` is equal to:
If `"sin"^-1("x"^2 - 7"x" + 12) = "n"pi, AA "n" in "I"`, then x = ____________.
If a = `(2sin theta)/(1 + costheta + sintheta)`, then `(1 + sintheta - costheta)/(1 + sintheta)` is
Which of the following functions is inverse of itself?
What will be the principal value of `sin^-1(-1/2)`?
Find the principal value of `tan^-1 (sqrt(3))`
Find the value, if sin–1x = y, then `->`:-
Values of tan–1 – sec–1(–2) is equal to
Value of `sin(pi/3 - sin^1 (- 1/2))` is equal to
What is the values of `cos^-1 (cos (7pi)/6)`
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) = ______.
If θ = `sin^-1((2x)/(1 + x^2)) + cos^-1((1 - x^2)/(1 + x^2))`, for `x ≥ 3/2` then the absolute value of `((cosθ + tanθ + 4)/secθ)` is ______.
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 = ______.
The value of `cos^-1(cos(π/2)) + cos^-1(sin((2π)/2))` is ______.
If y = `tan^-1 (sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2))`, then `dy/dx` is equal to ______.
If sin–1x – cos–1x = `π/6`, then x = ______.
Prove that:
tan–1x + tan–1y = `π + tan^-1((x + y)/(1 - xy))`, provided x > 0, y > 0, xy > 1
Find the value of `sin(2cos^-1 sqrt(5)/3)`.
Solve for x:
5tan–1x + 3cot–1x = 2π
