Advertisements
Advertisements
प्रश्न
Find the value of `cos^-1 (1/2) + tan^-1 (1/sqrt(3))`
Advertisements
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)`
`tan^(-1) sqrt3 - sec^(-1)(-2)` is equal to ______.
Find the domain of the following function:
`f(x) = sin^-1x + sinx`
Find the domain of the following function:
`f(x)sin^-1sqrt(x^2-1)`
Solve for x:
`tan^-1 [(x-1),(x-2)] + tan^-1 [(x+1),(x+2)] = x/4`
In ΔABC prove that `(b + c - a) tan "A"/(2) = (c + a - b)tan "B"/(2) = (a + b - c)tan "C"/(2)`.
Evaluate the following:
`cos^-1(1/2) + 2sin^-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)`
Find the principal solutions of the following equation:
cot 2θ = 0.
The principal value of cos−1`(-1/2)` is ______
Evaluate:
`sin[cos^-1 (3/5)]`
Find the principal value of the following:
`sec^-1 (-sqrt2)`
Prove that:
`tan^-1 (4/3) + tan^-1 (1/7) = pi/4`
Solve: tan-1 (x + 1) + tan-1 (x – 1) = `tan^-1 (4/7)`
Find the principal value of `sin^-1 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)`
The value of 2 `cot^-1 1/2 - cot^-1 4/3` is ______
If `sin^-1x + cos^-1y = (3pi)/10,` then `cos^-1x + sin^-1y =` ______
`tan[2tan^-1 (1/3) - pi/4]` = ______.
The value of cot (- 1110°) is equal to ______.
In a triangle ABC, ∠C = 90°, then the value of `tan^-1 ("a"/("b + c")) + tan^-1("b"/("c + a"))` is ______.
`cos(2sin^-1 3/4+cos^-1 3/4)=` ______.
Prove that `cot(pi/4 - 2cot^-1 3)` = 7
If 2 tan–1(cos θ) = tan–1(2 cosec θ), then show that θ = π 4, where n is any integer.
`("cos" 8° - "sin" 8°)/("cos" 8° + "sin" 8°)` is equal to ____________.
`"sin" 265° - "cos" 265°` is ____________.
If tan-1 3 + tan-1 x = tan-1 8, then x = ____________.
`"sin"^-1 (1/sqrt2)`
If 6sin-1 (x2 – 6x + 8.5) = `pi`, then x is equal to ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
`"cos"^-1 ["cos" (2 "cot"^-1 (sqrt2 - 1))] =` ____________.
The equation 2cos-1 x + sin-1 x `= (11pi)/6` has ____________.
`sin[π/3 - sin^-1 (-1/2)]` is equal to:
If |Z1| = |Z2| and arg (Z1) + arg (Z2) = 0, then
If `(-1)/sqrt(2) ≤ x ≤ 1/sqrt(2)` then `sin^-1 (2xsqrt(1 - x^2))` is equal to
`2tan^-1 (cos x) = tan^-1 (2"cosec" x)`, then 'x' will be equal to
If `sin(sin^-1 1/5 + cos^-1 x) = 1`, the what will be the value of x?
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 ax + b (sec (tan–1 x)) = c and ay + b (sec.(tan–1 y)) = c, then `(x + y)/(1 - xy)` = ______.
If 2 tan–1 (cosx) = tan–1 (2 cosec x), then sin x + cos x is equal to ______.
The value of `tan(cos^-1 4/5 + tan^-1 2/3)` is ______.
Find the value of `sin(2cos^-1 sqrt(5)/3)`.
Find the value of `tan^-1(x/y) + tan^-1((y - x)/(y + x))`
