Advertisements
Advertisements
प्रश्न
If tan–1x + tan–1y + tan–1z = π, show that x + y + z = xyz
उत्तर
tan–1x + tan–1y + tan–1z = π
`tan^-1 [(x + y)/(1 - xy)] + tan^-1z = pi`
`tan^-1 [((x + y)/(1 - xy) + z)/(1 - ((x + y)/(1 - xy))z)] = pi`
`tan^-1 [((x + y + z(1 - xy))/(1 - xy))/((1 - xy - (xz + yz))/(1 - xy))] = pi`
`(x + y + z - zyz)/(1 - xy - xz - yz) = tanpi` = 0
x + y + z – xyz = 0
x + y + z = xyz
APPEARS IN
संबंधित प्रश्न
Prove that `2tan^(-1)(1/5)+sec^(-1)((5sqrt2)/7)+2tan^(-1)(1/8)=pi/4`
If `tan^-1(2x)+tan^-1(3x)=pi/4`, then find the value of ‘x’.
Prove `2 tan^(-1) 1/2 + tan^(-1) 1/7 = tan^(-1) 31/17`
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 given expression.
`sin^(-1) (sin (2pi)/3)`
Find the value of the given expression.
`tan(sin^(-1) 3/5 + cot^(-1) 3/2)`
`sin[pi/3 - sin^(-1) (-1/2)]` is equal to ______.
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 [sin 5]`
Prove that `tan^-1x + tan^-1y + tan^-1z = tan^-1[(x + y + z - xyz)/(1 - xy - yz - zx)]`
Solve: `sin^-1 5/x + sin^-1 12/x = pi/2`
Evaluate: `tan^-1 sqrt(3) - sec^-1(-2)`.
If y = `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` for all x, then ______ < y < ______.
`"cot" (pi/4 - 2 "cot"^-1 3) =` ____________.
`"sin"^-1 (1/sqrt2)`
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:
𝐴' Is another viewer standing on the same line of observation across the road. If the width of the road is 5 meters, then the difference between ∠CAB and ∠CA'B is ______.
`tan^-1 1/2 + tan^-1 2/11` is equal to
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`
`50tan(3tan^-1(1/2) + 2cos^-1(1/sqrt(5))) + 4sqrt(2) tan(1/2tan^-1(2sqrt(2)))` is equal to ______.
