Advertisements
Advertisements
प्रश्न
`tan^-1 sqrt3 - cot^-1 (- sqrt3)` is equal to ______.
पर्याय
π
`-pi/2`
0
`2 sqrt3`
Advertisements
उत्तर
`tan^-1 sqrt3 - cot^-1 (- sqrt3)` is equal to `underlinebb(-pi/2)`.
Explanation:
⇒ `tan^-1 sqrt3 - cot^-1 (- sqrt3)`
= `tan^-1 (tan pi/3) - cot^-1 (-cot pi/6)`
= `pi/3 - cot^-1 [cot (pi - pi/6)]`
= `pi/3 - cot^-1 [cot ((5pi)/6)]`
= `pi/6 - (5 pi)/6`
= `(2pi - 5pi)/6`
= `-(3pi)/6`
= `- pi/2`
संबंधित प्रश्न
Prove that: `tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4`
Solve for x : tan-1 (x - 1) + tan-1x + tan-1 (x + 1) = tan-1 3x
Prove `2 tan^(-1) 1/2 + tan^(-1) 1/7 = tan^(-1) 31/17`
Write the following function in the simplest form:
`tan^(-1) (sqrt(1 + x^2) - 1)/x, x ≠ 0`
Write the function in the simplest form: `tan^(-1) 1/(sqrt(x^2 - 1)), |x| > 1`
Prove that `cos^(-1) 4/5 + cos^(-1) 12/13 = cos^(-1) 33/65`.
Prove that `cos^(-1) 12/13 + sin^(-1) 3/5 = sin^(-1) 56/65`.
If y = `(x sin^-1 x)/sqrt(1 -x^2)`, prove that: `(1 - x^2)dy/dx = x + y/x`
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)`.
Solve: tan-1 4 x + tan-1 6x `= π/(4)`.
Solve: `2tan^-1 (cos x) = tan^-1 (2"cosec" x)`
Choose the correct alternative:
If `sin^-1x + sin^-1y = (2pi)/3` ; then `cos^-1x + cos^-1y` is equal to
Evaluate: `tan^-1 sqrt(3) - sec^-1(-2)`.
Evaluate: `sin^-1 [cos(sin^-1 sqrt(3)/2)]`
Prove that cot–17 + cot–18 + cot–118 = cot–13
If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is ______.
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 `sin^-1 ((2"a")/(1 + "a"^2)) + cos^-1 ((1 - "a"^2)/(1 + "a"^2)) = tan^-1 ((2x)/(1 - x^2))`. where a, x ∈ ] 0, 1, then the value of x is ______.
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 < ______.
The value of cos215° - cos230° + cos245° - cos260° + cos275° is ______.
`"cot" (pi/4 - 2 "cot"^-1 3) =` ____________.
`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`
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 ____________.
The value of the expression tan `(1/2 "cos"^-1 2/sqrt3)`
`"cot" ("cosec"^-1 5/3 + "tan"^-1 2/3) =` ____________.
If sin `("sin"^-1 1/5 + "cos"^-1 "x") = 1,` then the value of x is ____________.
Solve for x : `"sin"^-1 2"x" + "sin"^-1 3"x" = pi/3`
The value of `"cos"^-1 ("cos" ((33pi)/5))` is ____________.
If `6"sin"^-1 ("x"^2 - 6"x" + 8.5) = pi,` then x is equal to ____________.
`"tan"^-1 (sqrt3)`
Solve for x : `{"x cos" ("cot"^-1 "x") + "sin" ("cot"^-1 "x")}^2` = `51/50
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 ∠DAB = ________.
`tan^-1 1/2 + tan^-1 2/11` is equal to
If `cos^-1(2/(3x)) + cos^-1(3/(4x)) = π/2(x > 3/4)`, then x is equal to ______.
Solve for x: `sin^-1(x/2) + cos^-1x = π/6`
