Advertisements
Advertisements
Question
Evaluate cot(tan−1(2x) + cot−1(2x))
Advertisements
Solution
cot(tan−1(2x) + cot−1(2x)) = `cot (pi/2)`
= 0 .......`[∵ tan^-1x + cot^-1 x = pi/2]`
RELATED QUESTIONS
Show that:
`cos^(-1)(4/5)+cos^(-1)(12/13)=cos^(-1)(33/65)`
Find the principal value of the following:
`sec^(-1) (2/sqrt(3))`
Find the principal value of the following:
`cot^(-1) (sqrt3)`
Find the principal value of the following:
`"cosec"^(-1)(-sqrt2)`
If sin−1 x = y, then ______.
If `sin^-1 x + sin^-1 y+sin^-1 z+sin^-1 t=2pi` , then find the value of x2 + y2 + z2 + t2
Evaluate the following:
`tan^-1(tan (5pi)/6)+cos^-1{cos((13pi)/6)}`
Find the set of values of `cosec^-1(sqrt3/2)`
Evaluate the following:
`\text(cosec)^-1(-2/sqrt3)+2cot^-1(-1)`
Solve for x:
`tan^-1 [(x-1),(x-2)] + tan^-1 [(x+1),(x+2)] = x/4`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of cosA
Prove the following:
`sin^-1(-1/2) + cos^-1(-sqrt(3)/2) = cos^-1(-1/2)`
Find the principal solutions of the following equation:
sin 2θ = `− 1/(sqrt2)`
Find the principal solutions of the following equation:
cot 2θ = 0.
The principal value of sin−1`(1/2)` is ______
If `sin(sin^-1(1/5) + cos^-1(x))` = 1, then x = ______
If tan−1x + tan−1y + tan−1z = π, then show that `1/(xy) + 1/(yz) + 1/(zx)` = 1
Prove that sin `[tan^-1 ((1 - x^2)/(2x)) + cos^-1 ((1 - x^2)/(1 + x^2))]` = 1
Prove that:
`tan^-1 (4/3) + tan^-1 (1/7) = pi/4`
Show that `tan^-1 (1/2) + tan^-1 (2/11) = tan^-1 (3/4)`
Evaluate:
`cos[tan^-1 (3/4)]`
Evaluate: sin`[1/2 cos^-1 (4/5)]`
Find the principal value of `sin^-1 1/sqrt(2)`
Find the principal value of `sec^-1 (- sqrt(2))`
Find the principal value of `tan^-1 (sqrt(3))`
A man standing directly opposite to one side of a road of width x meter views a circular shaped traffic green signal of diameter ‘a’ meter on the other side of the road. The bottom of the green signal Is ‘b’ meter height from the horizontal level of viewer’s eye. If ‘a’ denotes the angle subtended by the diameter of the green signal at the viewer’s eye, then prove that α = `tan^-1 (("a" + "b")/x) - tan^-1 ("b"/x)`
Choose the correct alternative:
cos 2θ cos 2ϕ+ sin2 (θ – ϕ) – sin2 (θ + ϕ) is equal to
The principle solutions of equation tan θ = -1 are ______
The principal value of `sin^-1 (sin (3pi)/4)` is ______.
If sin `(sin^-1 1/3 + cos^-1 x) = 1`, then the value of x is ______.
`tan[2tan^-1 (1/3) - pi/4]` = ______.
In a triangle ABC, ∠C = 90°, then the value of `tan^-1 ("a"/("b + c")) + tan^-1("b"/("c + a"))` is ______.
`(sin^-1(-1/2) + tan^-1(-1/sqrt(3)))/(sec^-1 (-2/sqrt(3)) + cos^-1(1/sqrt(2))` = ______.
If `3tan^-1x +cot^-1x = pi`, then xis equal to ______.
The domain of the function y = sin–1 (– x2) is ______.
If `"cos"^-1 "x + sin"^-1 "x" = pi`, then the value of x is ____________.
If 6sin-1 (x2 – 6x + 8.5) = `pi`, then x is equal to ____________.
The number of solutions of sin–1x + sin–1(1 – x) = cos–1x is
If `(-1)/sqrt(2) ≤ x ≤ 1/sqrt(2)` then `sin^-1 (2xsqrt(1 - x^2))` is equal to
Domain and Rariges of cos–1 is:-
Find the principal value of `cot^-1 ((-1)/sqrt(3))`
sin [cot–1 (cos (tan–1 x))] = ______.
Solve for x:
5tan–1x + 3cot–1x = 2π
Find the value of `tan^-1(x/y) + tan^-1((y - x)/(y + x))`
