Question

Difference between the greatest and least value of f(x) = `(1 + (cos^-1x)/π)^2 - (1 + (sin^-1x)/π)^2` is ______.

Options

• 4.00

• 5.00

• 6.00

• 7.00

Answer 1

Difference between the greatest and least value of f(x) = `(1 + (cos^-1x)/π)^2 - (1 + (sin^-1x)/π)^2` is 5.00.

Explanation:

f(x) = `(2 + (cos^-1x + sin^-1x)/π)((cos^-1x - sin^-1x)/π)`

f(x) = `(2 + (cos^-1x + sin^-1x)/π)((2cos^-1x)/π - 1/2)`

Greatest value = `(2 + 1/2)(2 - 1/2) = 15/4`

Least value = `5/2 xx (-1/2) = -5/4`

Difference = `15/4 + 5/4` = 5