Advertisements
Advertisements
Question
Find the value of `sin(2tan^-1 2/3) + cos(tan^-1 sqrt(3))`
Advertisements
Solution
Let `tan-1 2/3` = x and `tan^-1 sqrt(3)` = y
So that tan x = `2/3` and tan y = `sqrt(3)`
Therefore, `sin(2tan^-1 2/3) + cos(tan^-1 sqrt(3))`
= sin (2x) + cos y
= `(2tanx)/(1 + tan^2x)+/sqrt(1 +tan^2y)`
= `(2*2/3)/(1 + 4/9) + 1/( + sqrt((sqrt(3))^2`
= `12/13 +1/2`
= `37/26`.
APPEARS IN
RELATED QUESTIONS
Write the principal value of `tan^(-1)+cos^(-1)(-1/2)`
Find the principal value of the following:
`sin^-1(cos (3pi)/4)`
For the principal value, evaluate of the following:
`cos^-1 1/2 + 2 sin^-1 (1/2)`
For the principal value, evaluate of the following:
`tan^-1(-1)+cos^-1(-1/sqrt2)`
Find the principal value of the following:
`sec^-1(-sqrt2)`
Find the principal value of the following:
`sec^-1(2)`
For the principal value, evaluate the following:
`tan^-1sqrt3-sec^-1(-2)`
Find the principal value of the following:
`cosec^-1(-sqrt2)`
Find the principal value of the following:
cosec-1(-2)
Find the principal value of the following:
`\text(cosec)^-1(2/sqrt3)`
if sec-1 x = cosec-1 v. show that `1/x^2 + 1/y^2 = 1`
Solve for x, if:
tan (cos-1x) = `2/sqrt5`
Find the value of `tan^-1 (tan (9pi)/8)`.
Find value of tan (cos–1x) and hence evaluate `tan(cos^-1 8/17)`
The domain of sin–1 2x is ______.
The principal value of `sin^-1 ((-sqrt(3))/2)` is ______.
The value of `tan(cos^-1 3/5 + tan^-1 1/4)` is ______.
Find the value of `tan^-1 (tan (5pi)/6) +cos^-1(cos (13pi)/6)`
Find the value of `tan^-1 (- 1/sqrt(3)) + cot^-1(1/sqrt(3)) + tan^-1(sin((-pi)/2))`
Find the value of `tan^-1 (tan (2pi)/3)`
Find the value of the expression `sin(2tan^-1 1/3) + cos(tan^-1 2sqrt(2))`
Find the value of `4tan^-1 1/5 - tan^-1 1/239`
Which of the following is the principal value branch of cos–1x?
Which of the following is the principal value branch of cosec–1x?
The domain of the function defined by f(x) = `sin^-1 sqrt(x- 1)` is ______.
If tan–1x + tan–1y = `(4pi)/5`, then cot–1x + cot–1y equals ______.
The principal value of `tan^-1 sqrt(3)` is ______.
The value of expression `tan((sin^-1x + cos^-1x)/2)`, when x = `sqrt(3)/2` is ______.
The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is ______.
The minimum value of n for which `tan^-1 "n"/pi > pi/4`, n ∈ N, is valid is 5.
The period of the function f(x) = cos4x + tan3x is ____________.
The general solution of the equation `"cot" theta - "tan" theta = "sec" theta` is ____________ where `(n in I).`
If sin `("sin"^-1 1/5 + "cos"^-1 "x") = 1,` then the value of x is ____________.
Which of the following is the principal value branch of `"cos"^-1 "x"`
What is the value of x so that the seven-digit number 8439 × 53 is divisible by 99?
What is the principle value of `sin^-1 (1/sqrt(2))`?
What is the value of `tan^-1(1) cos^-1(- 1/2) + sin^-1(- 1/2)`
