Advertisements
Advertisements
प्रश्न
Solve for x : `tan^-1 ((2-"x")/(2+"x")) = (1)/(2)tan^-1 ("x")/(2), "x">0.`
उत्तर
Given that
⇒ `tan^-1 ((2-"x")/(2+"x")) = (1)/(2) tan^-1 ("x")/(2)`
⇒ `2tan^-1 ((2-"x")/(2+"x")) = tan^-1 ("x")/(2)`
⇒ `tan^-1 (2((2-"x")/(2+"x")))/(1 - ((2-"x")/(2+"x"))^2) = tan^-1 ("x")/(2)`
⇒ `tan^-1 (4 - x^2)/(4x) = tan^-1 ("x")/(2)`
⇒ `(4 -"x"^2)/(4"x") = ("x")/(2)`
∴ `"x" = 2/sqrt3 ...[∵ "x" >0]`.
APPEARS IN
संबंधित प्रश्न
sin–1 (1 – x) – 2 sin–1 x = `pi/2` , then x is equal to ______.
Solve for x : \[\cos \left( \tan^{- 1} x \right) = \sin \left( \cot^{- 1} \frac{3}{4} \right)\] .
If tan-1 x - cot-1 x = tan-1 `(1/sqrt(3)),`x> 0 then find the value of x and hence find the value of sec-1 `(2/x)`.
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 [sin 5]`
Find the value of the expression in terms of x, with the help of a reference triangle
`tan(sin^-1(x + 1/2))`
If tan–1x + tan–1y + tan–1z = π, show that x + y + z = xyz
Solve: `cot^-1 x - cot^-1 (x + 2) = pi/12, x > 0`
Choose the correct alternative:
`sin^-1 (tan pi/4) - sin^-1 (sqrt(3/x)) = pi/6`. Then x is a root of the equation
Choose the correct alternative:
If `cot^-1(sqrt(sin alpha)) + tan^-1(sqrt(sin alpha))` = u, then cos 2u is equal to
Evaluate: `sin^-1 [cos(sin^-1 sqrt(3)/2)]`
Show that `2tan^-1 {tan alpha/2 * tan(pi/4 - beta/2)} = tan^-1 (sin alpha cos beta)/(cosalpha + sinbeta)`
If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is ______.
Evaluate `cos[cos^-1 ((-sqrt(3))/2) + pi/6]`
Show that `tan(1/2 sin^-1 3/4) = (4 - sqrt(7))/3` and justify why the other value `(4 + sqrt(7))/3` is ignored?
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 ______.
The value of cos215° - cos230° + cos245° - cos260° + cos275° is ______.
If `"tan"^-1 ("cot" theta) = 2theta, "then" theta` is equal to ____________.
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 =` ____________.
Solve for x : `"sin"^-1 2"x" + "sin"^-1 3"x" = pi/3`
`"tan"^-1 (sqrt3)`
If `"sin" {"sin"^-1 (1/2) + "cos"^-1 "x"} = 1`, then the value of x is ____________.
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:
Measure of ∠EAB = ________.
Find the value of `cos^-1 (1/2) + 2sin^-1 (1/2) ->`:-
Find the value of `sin^-1 [sin((13π)/7)]`
`"tan" ^-1 sqrt3 - "cot"^-1 (- sqrt3)` is equal to ______.
Solve:
sin–1(x) + sin–1(1 – x) = cos–1x.
