Advertisements
Advertisements
प्रश्न
`sin^-1{cos(sin^-1 sqrt3/2)}`
उत्तर
`sin^-1{cos(sin^-1 sqrt3/2)}=sin^-1{cos(sin^-1 sin pi/3)}`
`=sin^-1{cos(pi/3)}`
`=sin^-1{1/2}`
`=sin^-1{sin pi/6}`
`=pi/6`
APPEARS IN
संबंधित प्रश्न
Find the principal value of `cot^(-1) (sqrt3)`
Find the value of the following:
`tan^(-1)(1) + cos^(-1) (-1/2) + sin^(-1) (-1/2)`
`tan^(-1) sqrt3 - sec^(-1)(-2)` is equal to ______.
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]
Find the domain of the following function:
`f(x) = sin^-1x + sinx`
Find the domain of the following function:
`f(x)=sin^-1x+sin^-1 2x`
Evaluate the following:
`tan^-1(-1/sqrt3)+tan^-1(-sqrt3)+tan^-1(sin(-pi/2))`
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)`
Evaluate the following:
`tan^-1(-1/sqrt3)+cot^-1(1/sqrt3)+tan^-1(sin(-pi/2))`
Prove that:
cot−1 7 + cot−1 8 + cot−1 18 = cot−1 3 .
Evaluate: tan `[ 2 tan^-1 (1)/(2) – cot^-1 3]`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of cos `A/2`
Find the principal value of the following: tan- 1( - √3)
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)`
Prove the following:
`tan^-1[sqrt((1 - cosθ)/(1 + cosθ))] = θ/(2)`, if θ ∈ (– π, π).
If tan−1x + tan−1y + tan−1z = π, then show that `1/(xy) + 1/(yz) + 1/(zx)` = 1
Show that `sin^-1(3/5) + sin^-1(8/17) = cos^-1(36/85)`
`sin^-1x + sin^-1 1/x + cos^-1x + cos^-1 1/x` = ______
Which of the following function has period 2?
The principal value of `tan^{-1(sqrt3)}` is ______
`cos^-1 4/5 + tan^-1 3/5` = ______.
The equation tan–1x – cot–1x = `(1/sqrt(3))` has ______.
Prove that `tan^-1 1/4 + tan^-1 2/9 = sin^-1 1/sqrt(5)`
When `"x" = "x"/2`, then tan x is ____________.
`"sin"^2 25° + "sin"^2 65°` is equal to ____________.
If 6sin-1 (x2 – 6x + 8.5) = `pi`, then x is equal to ____________.
If tan-1 x – tan-1 y = tan-1 A, then A is equal to ____________.
If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt "cos" alpha) = "x",` then sinx is equal to ____________.
If `sqrt(2)` sec θ + tan θ = 1, then the general value of θ is
Find the value, if sin–1x = y, then `->`:-
`2tan^-1 (cos x) = tan^-1 (2"cosec" x)`, then 'x' will be equal to
`lim_(n→∞)tan{sum_(r = 1)^n tan^-1(1/(1 + r + r^2))}` is equal to ______.
Let x = sin–1(sin8) + cos–1(cos11) + tan–1(tan7), and x = k(π – 2.4) for an integer k, then the value of k is ______.
Derivative of `tan^-1(x/sqrt(1 - x^2))` with respect sin–1(3x – 4x3) is ______.
Find the value of `cos(x/2)`, if tan x = `5/12` and x lies in third quadrant.
