Advertisements
Advertisements
प्रश्न
Evaluate:
`sin[cos^-1 (3/5)]`
उत्तर
Let x = `cos^-1 (3/5)` .......(i)
∴ cos x = `3/5`
∴ sin x = `sqrt(1 - cos^2x)`
= `sqrt(1 - 9/25)`
= `sqrt(16/25)`
= `4/5`
⇒ x = `sin^-1 (4/5)` .......(ii)
From (i) and (ii), we get
`sin [cos^-1 (3/5)] = sin[sin^-1 (4/5)]`
= `4/5`
APPEARS IN
संबंधित प्रश्न
Show that `2sin^-1(3/5) = tan^-1(24/7)`
Find the principal values of `sin^(-1) (-1/2)`
Find the value of the following:
`tan^(-1)(1) + cos^(-1) (-1/2) + sin^(-1) (-1/2)`
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]
Evaluate the following:
`tan^-1(tan (5pi)/6)+cos^-1{cos((13pi)/6)}`
Evaluate the following:
`cot^-1 1/sqrt3-\text(cosec)^-1(-2)+sec^-1(2/sqrt3)`
Evaluate the following:
`cot^-1{2cos(sin^-1 sqrt3/2)}`
Evaluate the following:
`\text(cosec)^-1(-2/sqrt3)+2cot^-1(-1)`
Solve for x:
`tan^-1 [(x-1),(x-2)] + tan^-1 [(x+1),(x+2)] = x/4`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of sin `(A/2)`.
In ΔABC, if a = 18, b = 24, c = 30 then find the values of sinA
Find the principal value of the following: cosec- 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:
`cos^-1(1/2) + 2sin^-1(1/2)`
Prove the following:
`sin^-1(3/5) + cos^-1(12/13) = sin^-1(56/65)`
Prove the following:
`tan^-1["cosθ + sinθ"/"cosθ - sinθ"] = pi/(4) + θ, if θ ∈ (- pi/4, pi/4)`
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)`
sin−1x − cos−1x = `pi/6`, then x = ______
If `sin(sin^-1(1/5) + cos^-1(x))` = 1, then x = ______
Evaluate cot(tan−1(2x) + cot−1(2x))
Find the value of `cos^-1 (1/2) + tan^-1 (1/sqrt(3))`
If tan−1x + tan−1y + tan−1z = π, then show that `1/(xy) + 1/(yz) + 1/(zx)` = 1
Find the principal value of the following:
`sin^-1 (- 1/2)`
Show that `tan^-1 (1/2) + tan^-1 (2/11) = tan^-1 (3/4)`
Express `tan^-1 [(cos x)/(1 - sin x)], - pi/2 < x < (3pi)/2` in the simplest form.
Find the principal value of cosec–1(– 1)
Choose the correct alternative:
cos 2θ cos 2ϕ+ sin2 (θ – ϕ) – sin2 (θ + ϕ) is equal to
The value of cot `(tan^-1 2x + cot^-1 2x)` is ______
lf `sqrt3costheta + sintheta = sqrt2`, then the general value of θ is ______
If `sin^-1(x/13) + cosec^-1(13/12) = pi/2`, then the value of x is ______
sin[3 sin-1 (0.4)] = ______.
Which of the following function has period 2?
If `sin^-1 3/5 + cos^-1 12/13 = sin^-1 P`, then P is equal to ______
The principal value of `tan^{-1(sqrt3)}` is ______
If 2tan-1 (cos x) = tan-1 (cosec2 x), then x = ______.
`tan[2tan^-1 (1/3) - pi/4]` = ______.
If `tan^-1x + tan^-1y = (4pi)/5`, then `cot^-1x + cot^-1y` equals ______.
The domain of the function defined by f(x) = sin–1x + cosx is ______.
Show that `cos(2tan^-1 1/7) = sin(4tan^-1 1/3)`
Prove that `tan^-1 1/4 + tan^-1 2/9 = sin^-1 1/sqrt(5)`
`"cos" 2 theta` is not equal to ____________.
If `"sin"^-1("x"^2 - 7"x" + 12) = "n"pi, AA "n" in "I"`, then x = ____________.
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 value of `"cos"^-1 ("cos" ((33 pi)/5))` is ____________.
`"tan"(pi/4 + 1/2 "cos"^-1 "x") + "tan" (pi/4 - 1/2 "cos"^-1 "x") =` ____________.
If tan-1 x – tan-1 y = tan-1 A, then A is equal to ____________.
`"cos" ["tan"^-1 {"sin" ("cot"^-1 "x")}]` is equal to ____________.
`"cos"^-1 ("cos" ((7pi)/6))` is equal to ____________.
If a = `(2sin theta)/(1 + costheta + sintheta)`, then `(1 + sintheta - costheta)/(1 + sintheta)` is
What will be the principal value of `sin^-1(-1/2)`?
What is the principal value of cosec–1(2).
Values of tan–1 – sec–1(–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
Value of `sin(pi/3 - sin^1 (- 1/2))` is equal to
If f(x) = x5 + 2x – 3, then (f–1)1 (–3) = ______.
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 = ______.
Number of values of x which lie in [0, 2π] and satisfy the equation
`(cos x/4 - 2sinx) sinx + (1 + sin x/4 - 2cosx)cosx` = 0
Derivative of `tan^-1(x/sqrt(1 - x^2))` with respect sin–1(3x – 4x3) is ______.
sin [cot–1 (cos (tan–1 x))] = ______.
If cos–1 x > sin–1 x, then ______.
Find the value of `cos(x/2)`, if tan x = `5/12` and x lies in third quadrant.
If –1 ≤ x ≤ 1, the prove that sin–1 x + cos–1 x = `π/2`
`sin[π/3 + sin^-1 (1/2)]` is equal to ______.
Prove that:
tan–1x + tan–1y = `π + tan^-1((x + y)/(1 - xy))`, provided x > 0, y > 0, xy > 1
The value of `tan(cos^-1 4/5 + tan^-1 2/3)` is ______.
Find the value of `sin(2cos^-1 sqrt(5)/3)`.
