Fill in the blanks If y = 2 tan –1 x + sin –1 for all x, then ____

Question

Fill in the blanks If y = 2 tan –1 x + sin –1 for all x, then ____ < y < ____.

Philoid · Accepted Answer

If y = 2 tan^–1 x + sin^–1 for all x, then -2π < y < 2π.

We know that,

So,

=4 tan^-1 x

So, y = 4 tan^-1 x

As, principal value of tan^-1 x is

So,

Hence, -2π < y < 2π

Fill in the blanksIf y = 2 tan–1 x + sin–1 for all x, then ____ < y < ____.