Advertisements
Advertisements
Question
Evaluate: `sin^-1 [cos(sin^-1 sqrt(3)/2)]`
Advertisements
Solution
`sin^-1 [cos(sin^-1 sqrt(3)/2)] = sin^-1[cos (pi/3)]`
= `sin^-1 [1/2]`
= `pi/6`.
APPEARS IN
RELATED QUESTIONS
If `sin (sin^(−1)(1/5)+cos^(−1) x)=1`, then find the value of x.
Prove that `cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2;x in (0,pi/4) `
Prove that `2tan^(-1)(1/5)+sec^(-1)((5sqrt2)/7)+2tan^(-1)(1/8)=pi/4`
Prove that `tan^(-1)((6x-8x^3)/(1-12x^2))-tan^(-1)((4x)/(1-4x^2))=tan^(-1)2x;|2x|<1/sqrt3`
Write the function in the simplest form: `tan^(-1) 1/(sqrt(x^2 - 1)), |x| > 1`
Write the function in the simplest form: `tan^(-1) ((cos x - sin x)/(cos x + sin x)) `,` 0 < x < pi`
Find the value of the following:
`tan^-1 [2 cos (2 sin^-1 1/2)]`
`sin[pi/3 - sin^(-1) (-1/2)]` is equal to ______.
Prove that:
`cos^(-1) 4/5 + cos^(-1) 12/13 = cos^(-1) 33/65`
Prove `tan^(-1) 1/5 + tan^(-1) (1/7) + tan^(-1) 1/3 + tan^(-1) 1/8 = pi/4`
sin (tan–1 x), |x| < 1 is equal to ______.
sin–1 (1 – x) – 2 sin–1 x = `pi/2`, then x is equal to ______.
Prove that `tan {pi/4 + 1/2 cos^(-1) a/b} + tan {pi/4 - 1/2 cos^(-1) a/b} = (2b)/a`
Solve the following equation for x: `cos (tan^(-1) x) = sin (cot^(-1) 3/4)`
Find the value, if it exists. If not, give the reason for non-existence
`tan^-1(sin(- (5pi)/2))`
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 [sin 5]`
Find the value of the expression in terms of x, with the help of a reference triangle
sin (cos–1(1 – x))
Find the value of `tan(sin^-1 3/5 + cot^-1 3/2)`
If tan–1x + tan–1y + tan–1z = π, show that x + y + z = xyz
Choose the correct alternative:
If `cot^-1(sqrt(sin alpha)) + tan^-1(sqrt(sin alpha))` = u, then cos 2u is equal to
If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is ______.
If α ≤ 2 sin–1x + cos–1x ≤ β, then ______.
The number of real solutions of the equation `sqrt(1 + cos 2x) = sqrt(2) cos^-1 (cos x)` in `[pi/2, pi]` is ______.
The minimum value of sinx - cosx is ____________.
If `"sec" theta = "x" + 1/(4 "x"), "x" in "R, x" ne 0,`then the value of `"sec" theta + "tan" theta` is ____________.
Solve for x : `"sin"^-1 2 "x" + sin^-1 3"x" = pi/3`
The value of `"tan"^ -1 (3/4) + "tan"^-1 (1/7)` is ____________.
The domain of the function defind by f(x) `= "sin"^-1 sqrt("x" - 1)` is ____________.
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 = "tan"^-1 1/8 =` ____________.
`"cos"^-1["cos"(2"cot"^-1(sqrt2 - 1))]` = ____________.
The value of `"cos"^-1 ("cos" ((33pi)/5))` is ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
Find the value of `cos^-1 (1/2) + 2sin^-1 (1/2) ->`:-
What is the simplest form of `tan^-1 sqrt(1 - x^2 - 1)/x, x ≠ 0`
Solve for x: `sin^-1(x/2) + cos^-1x = π/6`
If sin–1x + sin–1y + sin–1z = π, show that `x^2 - y^2 - z^2 + 2yzsqrt(1 - x^2) = 0`
