Advertisements
Advertisements
प्रश्न
Find the value of the given expression.
`tan(sin^(-1) 3/5 + cot^(-1) 3/2)`
Advertisements
उत्तर
`tan(sin^(-1) 3/5 + cot^(-1) 3/2)`
⇒ `sin^-1 3/5 = x`
⇒ `sin x = 3/5`
⇒ `cos x = sqrt(1 - sin^2 x) = 4/5`
⇒ `sec x = 5/4`
⇒ `tan x = sqrt(sec^2 - 1)`
⇒ `sqrt (25/16 - 1)`
⇒ `3/4`
⇒ `tan^-1 3/4`
⇒ `sin^-1 3/5 = tan^-1 3/4` ...(1)
⇒ `cot^-1 3/2 = tan^-1 2/3` ...(2)
⇒ `tan(sin^-1 3/5 + cot^-1 3/2)`
⇒ `tan (tan^-1 (((3/4 + 2/3))/(1 - 3/4 xx 2/3)))`
⇒ `tan (tan^-1 (((9 + 8)/12)/(1 - 1/2)))`
⇒ `tan(tan^-1 (17/6))`
= `17/6`
APPEARS IN
संबंधित प्रश्न
Prove that: `tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4`
Write the following function in the simplest form:
`tan^(-1) (sqrt(1 + x^2) - 1)/x, x ≠ 0`
if `tan^(-1) (x-1)/(x - 2) + tan^(-1) (x + 1)/(x + 2) = pi/4` then find the value of x.
Find the value of the given expression.
`sin^(-1) (sin (2pi)/3)`
Prove that `cot^(-1) ((sqrt(1 + sin x) + sqrt(1 - sinx))/(sqrt(1 + sin x) - sqrt(1 - sinx))) = x/2, x ∈ (0, pi/4)`.
Solve the following equation:
2 tan−1 (cos x) = tan−1 (2 cosec x)
sin (tan–1 x), |x| < 1 is equal to ______.
Solve `tan^(-1) - tan^(-1) (x - y)/(x+y)` is equal to
(A) `pi/2`
(B). `pi/3`
(C) `pi/4`
(D) `(-3pi)/4`
Prove that `3sin^(-1)x = sin^(-1) (3x - 4x^3)`, `x in [-1/2, 1/2]`
Solve for x : \[\tan^{- 1} \left( \frac{x - 2}{x - 1} \right) + \tan^{- 1} \left( \frac{x + 2}{x + 1} \right) = \frac{\pi}{4}\] .
Solve for x : `tan^-1 ((2-"x")/(2+"x")) = (1)/(2)tan^-1 ("x")/(2), "x">0.`
Prove that `tan^-1 2/11 + tan^-1 7/24 = tan^-1 1/2`
Simplify: `tan^-1 x/y - tan^-1 (x - y)/(x + y)`
Solve: `tan^-1x = cos^-1 (1 - "a"^2)/(1 + "a"^2) - cos^-1 (1 - "b"^2)/(1 + "b"^2), "a" > 0, "b" > 0`
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:
If `cot^-1(sqrt(sin alpha)) + tan^-1(sqrt(sin alpha))` = u, then cos 2u is equal to
If |x| ≤ 1, then `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` is equal to ______.
The number of real solutions of the equation `sqrt(1 + cos 2x) = sqrt(2) cos^-1 (cos x)` in `[pi/2, pi]` is ______.
If cos–1x > sin–1x, then ______.
The value of cos215° - cos230° + cos245° - cos260° + cos275° is ______.
The maximum value of sinx + cosx is ____________.
The minimum value of sinx - cosx is ____________.
The value of cot `("cosec"^-1 5/3 + "tan"^-1 2/3)` is ____________.
The domain of the function defind by f(x) `= "sin"^-1 sqrt("x" - 1)` is ____________.
`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 = "tan"^-1 1/8 =` ____________.
If x = a sec θ, y = b tan θ, then `("d"^2"y")/("dx"^2)` at θ = `π/6` is:
`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 + "tan"^-1 1/8 =` ____________.
`"cos"^-1["cos"(2"cot"^-1(sqrt2 - 1))]` = ____________.
`"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:
Measure of ∠CAB = ________.
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
The value of `tan^-1 (x/y) - tan^-1 (x - y)/(x + y)` is equal to
Find the value of `tan^-1 [2 cos (2 sin^-1 1/2)] + tan^-1 1`.
The value of cosec `[sin^-1((-1)/2)] - sec[cos^-1((-1)/2)]` is equal to ______.
Principal value of `"cosec"^(−1)((−2)/sqrt3)` is equal to ______.
