Advertisements
Advertisements
प्रश्न
In ΔABC, if a = 18, b = 24, c = 30 then find the values of tan `A/2`
Advertisements
उत्तर
Given : a = 18, b = 24 and c = 30
∴ 2s = a + b + c
= 18 + 24 + 30
= 72
∴ s = 36
`tan "A"/(2) = (sin "A"/2)/(cos "A"/2)`
= `((1)/sqrt(10))/((3)/sqrt(10)`
= `(1)/(3)`.
APPEARS IN
संबंधित प्रश्न
If `sin^-1(1-x) -2sin^-1x = pi/2` then x is
- -1/2
- 1
- 0
- 1/2
Find the principal value of the following:
`"cosec"^(-1)(-sqrt2)`
`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]
If `sin^-1 x + sin^-1 y+sin^-1 z+sin^-1 t=2pi` , then find the value of x2 + y2 + z2 + t2
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)`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of A(ΔABC)
In ΔABC prove that `(b + c - a) tan "A"/(2) = (c + a - b)tan "B"/(2) = (a + b - c)tan "C"/(2)`.
In ΔABC prove that `sin "A"/(2). sin "B"/(2). sin "C"/(2) = ["A(ΔABC)"]^2/"abcs"`
Prove the following:
`cos^-1(3/5) + cos^-1(4/5) = pi/(2)`
Find the principal solutions of the following equation:
sin 2θ = `− 1/(sqrt2)`
sin−1x − cos−1x = `pi/6`, then x = ______
Prove that sin `[tan^-1 ((1 - x^2)/(2x)) + cos^-1 ((1 - x^2)/(1 + x^2))]` = 1
Show that `sin^-1(3/5) + sin^-1(8/17) = cos^-1(36/85)`
Prove that `2 tan^-1 (1/8) + tan^-1 (1/7) + 2tan^-1 (1/5) = pi/4`
Find the principal value of `sin^-1 1/sqrt(2)`
Find the principal value of `tan^-1 (sqrt(3))`
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 `sin^-1 3/5 + cos^-1 12/13 = sin^-1 P`, then P is equal to ______
`tan[2tan^-1 (1/3) - pi/4]` = ______.
`cos(2sin^-1 3/4+cos^-1 3/4)=` ______.
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then θ = ______
If `tan^-1x + tan^-1y = (4pi)/5`, then `cot^-1x + cot^-1y` equals ______.
`(sin^-1(-1/2) + tan^-1(-1/sqrt(3)))/(sec^-1 (-2/sqrt(3)) + cos^-1(1/sqrt(2))` = ______.
The value of `cos(pi/4 + x) - cos(pi/4 - x)` is ______.
`"cos" 2 theta` is not equal to ____________.
`("cos" 8° - "sin" 8°)/("cos" 8° + "sin" 8°)` is equal to ____________.
`"sin"^-1 (-1/2)`
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
The value of `"cos"^-1 ("cos" ((33 pi)/5))` is ____________.
`"cos"^-1 ["cos" (2 "cot"^-1 (sqrt2 - 1))] =` ____________.
3 tan-1 a is equal to ____________.
`2"tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
If A = `[(cosx, sinx),(-sinx, cosx)]`, then A1 A–1 is
The number of solutions of sin–1x + sin–1(1 – x) = cos–1x is
If `sqrt(2)` sec θ + tan θ = 1, then the general value of θ is
What will be the principal value of `sin^-1(-1/2)`?
`tan^-1 (1 - x)/(1 + x) = 1/2tan^-1x, (x > 0)`, x then will be equal to.
If f'(x) = x–1, then find f(x)
`cot^-1(sqrt(cos α)) - tan^-1 (sqrt(cos α))` = x, then sin 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 tan–1 (2x) + tan–1 (3x) = `π/4`, then x = ______.
The value of `cos^-1(cos(π/2)) + cos^-1(sin((2π)/2))` is ______.
If sin–1x – cos–1x = `π/6`, then x = ______.
