Advertisements
Advertisements
Question
Evaluate the following:
`tan^-1(-1/sqrt3)+tan^-1(-sqrt3)+tan^-1(sin(-pi/2))`
Advertisements
Solution
`tan^-1(-1/sqrt3)+tan^-1(-sqrt3)+tan^-1(sin(-pi/2))`
= `tan^-1(-1/sqrt3)+tan^-1(-sqrt3)+tan^-1(sin(-pi/2))`
`=tan^-1(-1/sqrt3)+tan^-1(-sqrt3)+tan^-1(-1)`
`=-tan^-1(1/sqrt3)-tan^-1(sqrt3)-tan^-1(1)`
`=-tan^-1(tan pi/6)-tan^-1(pi/3)-tan^-1(pi/4)`
`=-pi/6-pi/3-pi/4`
`=-(3pi)/4`
APPEARS IN
RELATED QUESTIONS
Show that `2sin^-1(3/5) = tan^-1(24/7)`
Find the principal value of the following:
`cos^(-1) (-1/2)`
Find the principal value of the following:
`cos^(-1) (-1/sqrt2)`
Find the value of the following:
`tan^(-1)(1) + cos^(-1) (-1/2) + sin^(-1) (-1/2)`
Evaluate the following:
`tan^-1 1+cos^-1 (-1/2)+sin^-1(-1/2)`
Evaluate: tan `[ 2 tan^-1 (1)/(2) – cot^-1 3]`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of cosA
In ΔABC prove that `(b + c - a) tan "A"/(2) = (c + a - b)tan "B"/(2) = (a + b - c)tan "C"/(2)`.
In ΔABC prove that `sin "A"/(2). sin "B"/(2). sin "C"/(2) = ["A(ΔABC)"]^2/"abcs"`
Find the principal value of the following: tan- 1( - √3)
Prove the following:
`sin^-1(1/sqrt(2)) -3sin^-1(sqrt(3)/2) = -(3π)/(4)`
Prove the following:
`cos^-1(3/5) + cos^-1(4/5) = pi/(2)`
Prove the following:
`tan^-1(1/2) + tan^-1(1/3) = pi/(4)`
Find the principal solutions of the following equation:
cot 2θ = 0.
Evaluate `cos[pi/6 + cos^-1 (- sqrt(3)/2)]`
If tan−1x + tan−1y + tan−1z = π, then show that `1/(xy) + 1/(yz) + 1/(zx)` = 1
Show that `tan^-1 (1/2) + tan^-1 (2/11) = tan^-1 (3/4)`
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
sin[3 sin-1 (0.4)] = ______.
In a triangle ABC, ∠C = 90°, then the value of `tan^-1 ("a"/("b + c")) + tan^-1("b"/("c + a"))` is ______.
Prove that `cot(pi/4 - 2cot^-1 3)` = 7
`("cos" 8° - "sin" 8°)/("cos" 8° + "sin" 8°)` is equal to ____________.
`"sin" 265° - "cos" 265°` is ____________.
`"sin" ["cot"^-1 {"cos" ("tan"^-1 "x")}] =` ____________.
The range of sin-1 x + cos-1 x + tan-1 x is ____________.
If |Z1| = |Z2| and arg (Z1) + arg (Z2) = 0, then
What is the value of `sin^-1(sin (3pi)/4)`?
What is the values of `cos^-1 (cos (7pi)/6)`
Find the principal value of `cot^-1 ((-1)/sqrt(3))`
Let x = sin–1(sin8) + cos–1(cos11) + tan–1(tan7), and x = k(π – 2.4) for an integer k, then the value of k is ______.
If tan–1 (2x) + tan–1 (3x) = `π/4`, then x = ______.
`(tan^-1 (sqrt(3)) - sec^-1(-2))/("cosec"^-1(-sqrt(2)) + cos^-1(-1/2))` is equal to ______.
If y = `tan^-1 (sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2))`, then `dy/dx` is equal to ______.
Prove that:
tan–1x + tan–1y = `π + tan^-1((x + y)/(1 - xy))`, provided x > 0, y > 0, xy > 1
The value of `tan(cos^-1 4/5 + tan^-1 2/3)` is ______.
If tan 4θ = `tan(2/θ)`, then the general value of θ is ______.
Find the value of `tan^-1(x/y) + tan^-1((y - x)/(y + x))`
