Question

Find the range of f(x) = sin^-1x = sec^-1x + tan^-1x

Answer 1

The function f is defined for x = ±1

Now, f(1) = sin^-1(1) + sec^-1(1) + tan^-1(1)

= π/2 + 0 + π/4 = 3π/4

Also, f(-1) = sin^-1(-1) + sec^-1(-1) + tan^-1(-1)

= - π/2 + π - 0 - π/4

= 3π/4

Thus, R_f = {π/4, 3π/4}