Advertisements
Advertisements
प्रश्न
If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is ______.
विकल्प
`pi/5`
`(2pi)/5`
`(3pi)/5`
`(4pi)/5`
Advertisements
उत्तर
If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is `(2pi)/5`.
Explanation:
We know tan–1x + cot–1x = `pi/2`.
Therefore cot–1x = `pi/2 - pi/10`
⇒ cot–1x = `pi/2 - pi/10 = (2pi)/5`.
APPEARS IN
संबंधित प्रश्न
Prove that: `tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4`
If `tan^-1(2x)+tan^-1(3x)=pi/4`, then find the value of ‘x’.
Prove `tan^(-1) 2/11 + tan^(-1) 7/24 = tan^(-1) 1/2`
Write the following function in the simplest form:
`tan^(-1) ((3a^2 x - x^3)/(a^3 - 3ax^2)), a > 0; (-a)/sqrt(3) < x < a/sqrt(3)`
Find the value of the following:
`tan 1/2 [sin^(-1) (2x)/(1 + x^2) + cos^(-1) (1 - y^2)/(1 + y^2)], |x| < 1, y > 0 and xy < 1`
Find the value of the given expression.
`sin^(-1) (sin (2pi)/3)`
`sin[pi/3 - sin^(-1) (-1/2)]` is equal to ______.
Prove that `cos^(-1) 4/5 + cos^(-1) 12/13 = cos^(-1) 33/65`.
Prove `(9pi)/8 - 9/4 sin^(-1) 1/3 = 9/4 sin^(-1) (2sqrt2)/3`
Find: ∫ sin x · log cos x dx
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 (cos pi)`
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 [sin 5]`
Find the value of `sin^-1[cos(sin^-1 (sqrt(3)/2))]`
Prove that `sin^-1 3/5 - cos^-1 12/13 = sin^-1 16/65`
If tan–1x + tan–1y + tan–1z = π, show that x + y + z = xyz
Choose the correct alternative:
`sin^-1 (tan pi/4) - sin^-1 (sqrt(3/x)) = pi/6`. Then x is a root of the equation
Evaluate `cos[sin^-1 1/4 + sec^-1 4/3]`
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 ______.
If y = `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` for all x, then ______ < y < ______.
The value of cot–1(–x) for all x ∈ R in terms of cot–1x is ______.
The maximum value of sinx + cosx is ____________.
The value of `"tan"^ -1 (3/4) + "tan"^-1 (1/7)` is ____________.
If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt"cos" alpha) = "x",` the sinx is equal to ____________.
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)`
The value of `"tan"^-1 (3/4) + "tan"^-1 (1/7)` is ____________.
`"cos"^-1["cos"(2"cot"^-1(sqrt2 - 1))]` = ____________.
The value of `"cos"^-1 ("cos" ((33pi)/5))` is ____________.
`"tan"^-1 (sqrt3)`
`"cos"^-1 (1/2)`
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 = ________.
What is the simplest form of `tan^-1 sqrt(1 - x^2 - 1)/x, x ≠ 0`
If sin–1x + sin–1y + sin–1z = π, show that `x^2 - y^2 - z^2 + 2yzsqrt(1 - x^2) = 0`
Principal value of `"cosec"^(−1)((−2)/sqrt3)` is equal to ______.
