Advertisements
Advertisements
प्रश्न
Find the value of `cos^-1 (1/2) + tan^-1 (1/sqrt(3))`
उत्तर
Let `cos^-1 (1/2)` = x
∴ cos x = `1/2`
= `cos pi/3`
The principal value branch of cos−1 is [0, π] and `0 ≤ pi/3 ≤ pi`
∴ x = `pi/3`
∴ `cos^-1 1/2 = pi/3`
Let `tan^-1 (1/sqrt(3))` = y
∴ tan y = `1/sqrt(3`
= tan `pi/6`
The principal value branch of tan−1 is `((-pi)/2, pi/2)` and `- pi/2, < pi/6 < pi/2`
∴ y = `pi/6`
∴ `tan^-1 (1/sqrt(3)) = pi/6`
∴ `cos^-1 (1/2) + tan^-1 (1/sqrt(3)) = pi/3 + pi/6`
= `(3pi)/6`
= `pi/2`
APPEARS IN
संबंधित प्रश्न
Show that:
`cos^(-1)(4/5)+cos^(-1)(12/13)=cos^(-1)(33/65)`
Find the principal values of `sin^(-1) (-1/2)`
Find the principal value of `cos^(-1) (sqrt3/2)`
Find the principal value of cosec−1 (2)
Find the principal value of `tan^(-1) (-sqrt3)`
Find the principal value of tan−1 (−1)
Find the principal value of `cot^(-1) (sqrt3)`
Find the principal value of `cos^(-1) (-1/sqrt2)`
Find the principal value of `cosec^(-1)(-sqrt2)`
`tan^(-1) sqrt3 - sec^(-1)(-2)` is equal to ______.
`sin^-1 1/2-2sin^-1 1/sqrt2`
Find the domain of the following function:
`f(x) = sin^-1x + sinx`
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:
`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)`
Evaluate the following:
`\text(cosec)^-1(-2/sqrt3)+2cot^-1(-1)`
Prove that:
cot−1 7 + cot−1 8 + cot−1 18 = cot−1 3 .
In ΔABC prove that `(b + c - a) tan "A"/(2) = (c + a - b)tan "B"/(2) = (a + b - c)tan "C"/(2)`.
Find the principal value of the following: `sin^-1 (1/2)`
Evaluate the following:
`tan^-1 sqrt(3) - sec^-1 (-2)`
Prove the following:
`sin^-1(3/5) + cos^-1(12/13) = sin^-1(56/65)`
Prove the following:
`tan^-1[sqrt((1 - cosθ)/(1 + cosθ))] = θ/(2)`, if θ ∈ (– π, π).
In ΔABC, prove the following:
`(cos A)/a + (cos B)/b + (cos C)/c = (a^2 + b^2 + c^2)/(2abc)`
Find the principal solutions of the following equation:
sin 2θ = `− 1/(sqrt2)`
sin−1x − cos−1x = `pi/6`, then x = ______
The principal value of cos−1`(-1/2)` is ______
`tan^-1(tan (7pi)/6)` = ______
If `sin(sin^-1(1/5) + cos^-1(x))` = 1, then x = ______
Evaluate cot(tan−1(2x) + cot−1(2x))
Prove that `2 tan^-1 (3/4) = tan^-1(24/7)`
Prove that sin `[tan^-1 ((1 - x^2)/(2x)) + cos^-1 ((1 - x^2)/(1 + x^2))]` = 1
Prove that cot−1(7) + 2 cot−1(3) = `pi/4`
Prove that `2 tan^-1 (1/8) + tan^-1 (1/7) + 2tan^-1 (1/5) = pi/4`
Find the principal value of the following:
`sin^-1 (- 1/2)`
Find the principal value of the following:
cosec-1 (2)
Evaluate:
`cos[tan^-1 (3/4)]`
Evaluate: `cos (sin^-1 (4/5) + sin^-1 (12/13))`
Find the principal value of `cos^-1 sqrt(3)/2`
Choose the correct alternative:
cos 2θ cos 2ϕ+ sin2 (θ – ϕ) – sin2 (θ + ϕ) is equal to
`sin^-1x + sin^-1 1/x + cos^-1x + cos^-1 1/x` = ______
In ΔABC, tan`A/2 = 5/6` and tan`C/2 = 2/5`, then ______
If `sin^-1(x/13) + cosec^-1(13/12) = pi/2`, then the value of x is ______
If 2tan-1 (cos x) = tan-1 (cosec2 x), then x = ______.
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 ______
If `tan^-1x + tan^-1y = (4pi)/5`, then `cot^-1x + cot^-1y` equals ______.
`sin{tan^-1((1 - x^2)/(2x)) + cos^-1((1 - x^2)/(1 + x^2))}` is equal to ______
The value of `sin^-1[cos(pi/3)] + sin^-1[tan((5pi)/4)]` is ______.
The domain of the function y = sin–1 (– x2) 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)`
`"sin"^2 25° + "sin"^2 65°` is equal to ____________.
If `"cos"^-1 "x + sin"^-1 "x" = pi`, then the value of x is ____________.
If tan-1 3 + tan-1 x = tan-1 8, then x = ____________.
The value of `"cos"^-1 ("cos" ((33 pi)/5))` is ____________.
Find the value of sec2 (tan-1 2) + cosec2 (cot-1 3) ____________.
If `"x" in (- pi/2, pi/2), "then the value of tan"^-1 ("tan x"/4) + "tan"^-1 ((3 "sin" 2 "x")/(5 + 3 "cos" 2 "x"))` is ____________.
`2"tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
The number of solutions of sin–1x + sin–1(1 – x) = cos–1x is
If `sqrt(2)` sec θ + tan θ = 1, then the general value of θ is
The inverse of `f(x) = sqrt(3x^2 - 4x + 5)` is
If `(-1)/sqrt(2) ≤ x ≤ 1/sqrt(2)` then `sin^-1 (2xsqrt(1 - x^2))` is equal to
What is the value of `sin^-1(sin (3pi)/4)`?
Domain and Rariges of cos–1 is:-
What is the principal value of cosec–1(2).
`sin(tan^-1x), |x| < 1` is equal to
`2tan^-1 (cos x) = tan^-1 (2"cosec" x)`, then 'x' will be equal to
Value of `sin(pi/3 - sin^1 (- 1/2))` is equal to
If sin–1a + sin–1b + sin–1c = π, then find the value of `asqrt(1 - a^2) + bsqrt(1 - b^2) + csqrt(1 - c^2)`.
If x ∈ R – {0}, then `tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2)))`
`(tan^-1 (sqrt(3)) - sec^-1(-2))/("cosec"^-1(-sqrt(2)) + cos^-1(-1/2))` is equal to ______.
sin [cot–1 (cos (tan–1 x))] = ______.
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 ______.
Find the value of `cos(x/2)`, if tan x = `5/12` and x lies in third quadrant.
Solve for x:
5tan–1x + 3cot–1x = 2π
