Advertisements
Advertisements
Questions
For the principal value, evaluate of the following:
`cos^-1 1/2 + 2 sin^-1 (1/2)`
Evaluate: `cos^-1 (1/2) + 2 sin^-1 (1/2)`
Advertisements
Solution
cos–1 (cos x) = x
sin–1 (sin x) = x
`cos^-1 1/2 + 2sin^-1 (1/2)`
= `cos^-1 (cos π/3) + 2 sin^-1 (sin π/6)`
= `π/3 + 2(π/6)`
= `(2π)/3`
RELATED QUESTIONS
The principal solution of `cos^-1(-1/2)` is :
Prove that `sin^(-1) (3/5) + cos^(-1) (12/13) = sin^(-1) (56/65)`
Solve `3tan^(-1)x + cot^(-1) x = pi`
Find the principal value of the following:
`sin^-1((sqrt3-1)/(2sqrt2))`
Find the principal value of the following:
`sin^-1((sqrt3+1)/(2sqrt2))`
Find the principal value of the following:
`sec^-1(2tan (3pi)/4)`
For the principal value, evaluate the following:
`sin^-1(-sqrt3/2)+\text{cosec}^-1(-2/sqrt3)`
Find the principal value of the following:
`cot^-1(-sqrt3)`
Find the principal value of the following:
`cot^-1(tan (3pi)/4)`
Show that `"sin"^-1(5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`
Solve for x, if:
tan (cos-1x) = `2/sqrt5`
Find the value of `cos^-1(cos (13pi)/6)`.
Find the value of `sin(2tan^-1 2/3) + cos(tan^-1 sqrt(3))`
The principal value branch of sec–1 is ______.
One branch of cos–1 other than the principal value branch corresponds to ______.
The value of cot (sin–1x) is ______.
The greatest and least values of (sin–1x)2 + (cos–1x)2 are respectively ______.
The value of sin (2 sin–1 (.6)) is ______.
Find the value of `tan^-1 (tan (5pi)/6) +cos^-1(cos (13pi)/6)`
Find the value of `tan^-1 (tan (2pi)/3)`
Which of the following is the principal value branch of cos–1x?
The value of `sin^-1 [cos((33pi)/5)]` is ______.
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to ______.
The value of sin (2 tan–1(0.75)) is equal to ______.
The value of `cot[cos^-1 (7/25)]` is ______.
The value of `sin^-1 (sin (3pi)/5)` is ______.
The set of values of `sec^-1 (1/2)` is ______.
The principal value of `tan^-1 sqrt(3)` is ______.
The value of `cos^-1 (cos (14pi)/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.
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)`
