The number of integral values of `k` for which the equation `sin^(-1)x+tan^(-1)x=2k+1` has a solution is

Options

A. (a) 1
B. (b) 2
C. (c) 3
D. (d) 4

Answer

B

Explanation

Given `sin^(-1) x + tan^(1) x = 2k + 1`
Both `sin^(-1) and tan^(-1)` are increasing functions. So `f(x)` is increasing function
The range of the function `sin^(-1) x + tan^(-1) x " is " [f(-1), f(1)]`
or `[(-3pi)/(4), (3pi)/(4)]`
Therefore, the integral values of `k` are `-1 adn 0`