Advertisements
Advertisements
प्रश्न
Find the principal value of `cos^-1 sqrt(3)/2`
उत्तर
Let y = `cos^-1 (sqrt(3)/2)`
Where 0 ≤ y ≤ π
cos y = `sqrt(3)/2`
= `cos (pi/6)`
y = `pi/6`
∴ The principal value of `cos^-1 sqrt(3)/2 = pi/6`
APPEARS IN
संबंधित प्रश्न
Find the value of the following:
`tan^(-1) (tan (7x)/6)`
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 principal value of the following: cos- 1`(-1/2)`
Find the principal solutions of the following equation:
sin 2θ = `− 1/(sqrt2)`
The principal value of cos−1`(-1/2)` is ______
Find the principal value of the following:
tan-1 (-1)
Find the principal value of `sec^-1 (- sqrt(2))`
A man standing directly opposite to one side of a road of width x meter views a circular shaped traffic green signal of diameter ‘a’ meter on the other side of the road. The bottom of the green signal Is ‘b’ meter height from the horizontal level of viewer’s eye. If ‘a’ denotes the angle subtended by the diameter of the green signal at the viewer’s eye, then prove that α = `tan^-1 (("a" + "b")/x) - tan^-1 ("b"/x)`
If 2tan-1 (cos x) = tan-1 (cosec2 x), then x = ______.
The value of `sin^-1(cos (53pi)/5)` is ______
If 2 tan–1(cos θ) = tan–1(2 cosec θ), then show that θ = π 4, where n is any integer.
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 ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
`sin[π/3 - sin^-1 (-1/2)]` is equal to:
`"cos" ["tan"^-1 {"sin" ("cot"^-1 "x")}]` is equal to ____________.
The equation of the tangent to the curve given by x = a sin3t, y = bcos3t at a point where t = `pi/2` is
Find the principal value of `tan^-1 (sqrt(3))`
If `sin(sin^-1 1/5 + cos^-1 x) = 1`, the what will be the value of x?