Advertisements
Advertisements
प्रश्न
Write the following function in the simplest form:
`tan^-1 ((cos x - sin x)/(cos x + sin x)), (-pi)/4 < x < (3 pi)/4`
Advertisements
उत्तर
`tan^-1 ((cos x - sin x)/(cos x + sin x))`
= `tan^-1 ((1 - sin x/cos x)/(1 + sin x/cos x))`
= `tan^-1 ((1 - tan x)/(1 + tan x))`
= tan−1 (1) − tan−1 (tan x)
= `pi/4 - x`
संबंधित प्रश्न
Prove that:
`tan^(-1)""1/5+tan^(-1)""1/7+tan^(-1)""1/3+tan^(-1)""1/8=pi/4`
If `tan^-1(2x)+tan^-1(3x)=pi/4`, then find the value of ‘x’.
Prove the following:
3cos−1x = cos−1(4x3 − 3x), `x ∈ [1/2, 1]`
Write the following function in the simplest form:
`tan^(-1) x/(sqrt(a^2 - x^2))`, |x| < a
Find the value of `cot(tan^(-1) a + cot^(-1) a)`
if `sin(sin^(-1) 1/5 + cos^(-1) x) = 1` then find the value of x
Find the value of the given expression.
`tan(sin^(-1) 3/5 + cot^(-1) 3/2)`
Prove that:
`cos^(-1) 12/13 + sin^(-1) 3/5 = sin^(-1) 56/65`
Prove `(9pi)/8 - 9/4 sin^(-1) 1/3 = 9/4 sin^(-1) (2sqrt2)/3`
sin–1 (1 – x) – 2 sin–1 x = `pi/2`, then x is equal to ______.
Find the value of `tan(sin^-1 3/5 + cot^-1 3/2)`
Prove that `tan^-1 2/11 + tan^-1 7/24 = tan^-1 1/2`
If tan–1x + tan–1y + tan–1z = π, show that x + y + z = xyz
Simplify: `tan^-1 x/y - tan^-1 (x - y)/(x + y)`
Solve: `sin^-1 5/x + sin^-1 12/x = pi/2`
Find the number of solutions of the equation `tan^-1 (x - 1) + tan^-1x + tan^-1(x + 1) = tan^-1(3x)`
Choose the correct alternative:
`tan^-1 (1/4) + tan^-1 (2/9)` is equal to
Prove that `tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/((1 + x^2) - sqrt(1 - x^2))) = pi/2 + 1/2 cos^-1x^2`
Prove that `sin^-1 8/17 + sin^-1 3/5 = sin^-1 7/85`
The number of real solutions of the equation `sqrt(1 + cos 2x) = sqrt(2) cos^-1 (cos x)` in `[pi/2, pi]` is ______.
If y = `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` for all x, then ______ < y < ______.
If `"sec" theta = "x" + 1/(4 "x"), "x" in "R, x" ne 0,`then the value of `"sec" theta + "tan" theta` is ____________.
The value of `"tan"^-1 (1/2) + "tan"^-1 (1/3) + "tan"^-1 (7/8)` is ____________.
`"cot" (pi/4 - 2 "cot"^-1 3) =` ____________.
`"sin" {2 "cos"^-1 ((-3)/5)}` is equal to ____________.
`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 + "tan"^-1 1/8 =` ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
`"tan"^-1 (sqrt3)`
`"cos"^-1 (1/2)`
`"sin"^-1 ((-1)/2)`
If `"sin" {"sin"^-1 (1/2) + "cos"^-1 "x"} = 1`, then the value of x is ____________.
If `"sin"^-1 (1 - "x") - 2 "sin"^-1 ("x") = pi/2,` then x is equal to ____________.
The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. “A” is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby. Ram, Robert and Rahim suggested to the firm to place the hoarding board at three different locations namely C, D and E. “C” is at the height of 10 metres from the ground level. For viewer A, the angle of elevation of “D” is double the angle of elevation of “C” The angle of elevation of “E” is triple the angle of elevation of “C” for the same viewer. Look at the figure given and based on the above information answer the following:
Measure of ∠EAB = ________.
`50tan(3tan^-1(1/2) + 2cos^-1(1/sqrt(5))) + 4sqrt(2) tan(1/2tan^-1(2sqrt(2)))` is equal to ______.
If `cos^-1(2/(3x)) + cos^-1(3/(4x)) = π/2(x > 3/4)`, then x is equal to ______.
Solve:
sin–1 (x) + sin–1 (1 – x) = cos–1 x
