Advertisements
Advertisements
Question
The value of the expression `2 sec^-1 2 + sin^-1 (1/2)` is ______.
Options
`pi/6`
`(5pi)/6`
`(7pi)/6`
1
Solution
The value of the expression `2 sec^-1 2 + sin^-1 (1/2)` is `(5pi)/6`.
Explanation:
`2 sec^-1 2 + sin^-1 1/2 = 2sec^-1 (sec pi/3) + sin^-1 (sin pi/6)`
= `2 * pi/3 + pi/6`
= `(2pi)/3 + pi/6`
= `(5pi)/6`
APPEARS IN
RELATED QUESTIONS
Write the principal value of `tan^(-1)+cos^(-1)(-1/2)`
Find the value of `tan^(-1) sqrt3 - cot^(-1) (-sqrt3)`
if `tan^(-1) a + tan^(-1) b + tan^(-1) x = pi`, prove that a + b + c = abc
Find the principal value of the following:
`sin^-1(cos (3pi)/4)`
Find the principal value of the following:
`tan^-1(-1/sqrt3)`
Find the principal value of the following:
`cot^-1(sqrt3)`
Find the value of `cos^-1(cos (13pi)/6)`.
Find the value of `tan^-1 (tan (9pi)/8)`.
Prove that tan(cot–1x) = cot(tan–1x). State with reason whether the equality is valid for all values of x.
The greatest and least values of (sin–1x)2 + (cos–1x)2 are respectively ______.
Let θ = sin–1 (sin (– 600°), then value of θ is ______.
If sin–1x + sin–1y = `pi/2`, then value of cos–1x + cos–1y is ______.
Find the value of `tan^-1 (tan (2pi)/3)`
Which of the following is the principal value branch of cos–1x?
Which of the following is the principal value branch of cosec–1x?
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to ______.
If tan–1x + tan–1y = `(4pi)/5`, then cot–1x + cot–1y equals ______.
The principal value of `cos^-1 (- 1/2)` is ______.
The value of `sin^-1 (sin (3pi)/5)` is ______.
If `cos(tan^-1x + cot^-1 sqrt(3))` = 0, then value of x is ______.
The principal value of `tan^-1 sqrt(3)` is ______.
The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is ______.
`2 "cos"^-1 "x = sin"^-1 (2"x" sqrt(1 - "x"^2))` is true for ____________.
`"cos" ["tan"^-1 {"sin" ("cot"^-1 "x")}]` is equal to ____________.
If `"tan"^-1 ("a"/"x") + "tan"^-1 ("b"/"x") = pi/2,` then x is equal to ____________.
`"sec" {"tan"^-1 (-"y"/3)}` is equal to ____________.
What is the principle value of `sin^-1 (1/sqrt(2))`?
