Advertisements
Advertisements
Question
If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is ______.
Options
`pi/5`
`(2pi)/5`
`(3pi)/5`
`(4pi)/5`
Advertisements
Solution
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
RELATED QUESTIONS
If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.
Write the following function in the simplest form:
`tan^(-1) (sqrt(1+x^2) -1)/x`, x ≠ 0
if `sin(sin^(-1) 1/5 + cos^(-1) x) = 1` then find the value of x
Find the value of the given expression.
`sin^(-1) (sin (2pi)/3)`
`cos^(-1) (cos (7pi)/6)` is equal to ______.
`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 that:
`cos^(-1) 12/13 + sin^(-1) 3/5 = sin^(-1) 56/65`
Solve the following equation:
2 tan−1 (cos x) = tan−1 (2 cosec x)
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 `tan {pi/4 + 1/2 cos^(-1) a/b} + tan {pi/4 - 1/2 cos^(-1) a/b} = (2b)/a`
Solve for x : \[\cos \left( \tan^{- 1} x \right) = \sin \left( \cot^{- 1} \frac{3}{4} \right)\] .
If cos-1 x + cos -1 y + cos -1 z = π , prove that x2 + y2 + z2 + 2xyz = 1.
Find the value of `tan(sin^-1 3/5 + cot^-1 3/2)`
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:
The equation tan–1x – cot–1x = `tan^-1 (1/sqrt(3))` has
Evaluate: `tan^-1 sqrt(3) - sec^-1(-2)`.
Prove that `2sin^-1 3/5 - tan^-1 17/31 = pi/4`
Show that `2tan^-1 {tan alpha/2 * tan(pi/4 - beta/2)} = tan^-1 (sin alpha cos beta)/(cosalpha + sinbeta)`
Evaluate `cos[cos^-1 ((-sqrt(3))/2) + pi/6]`
Prove that `tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/((1 + x^2) - sqrt(1 - x^2))) = pi/2 + 1/2 cos^-1x^2`
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 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 cot `("cosec"^-1 5/3 + "tan"^-1 2/3)` is ____________.
If `"tan"^-1 (("x" - 1)/("x" + 2)) + "tan"^-1 (("x" + 1)/("x" + 2)) = pi/4,` then x is equal to ____________.
Solve for x : `"sin"^-1 2"x" + "sin"^-1 3"x" = pi/3`
The value of `"tan"^-1 (3/4) + "tan"^-1 (1/7)` is ____________.
`"tan"^-1 (sqrt3)`
`"sin"^-1 ((-1)/2)`
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 ∠EAB = ________.
Find the value of `cos^-1 (1/2) + 2sin^-1 (1/2) ->`:-
`sin^-1(1 - x) - 2sin^-1 x = pi/2`, tan 'x' is equal to
If `cos^-1(2/(3x)) + cos^-1(3/(4x)) = π/2(x > 3/4)`, then x is equal to ______.
Write the following function in the simplest form:
`tan^-1 ((cos x - sin x)/(cos x + sin x)), (-pi)/4 < x < (3 pi)/4`
If \[\tan^{-1}\left(\frac{x}{2}\right)+\tan^{-1}\left(\frac{y}{2}\right)+\tan^{-1}\left(\frac{z}{2}\right)=\frac{\pi}{2}\] then xy + yz + zx =
