Question

How do you solve `cot [Arcsin (-12/13)]`?

Answer 1

`-5/12` against the principal value of `arc sin (-123/13)` and, for the general value, the answer is `+-5/12`.

Explanation:

Let `a = arc sin (-12/13)`. Then, `sin a = -12/13<0`. The principal

value of a is in the 4th quadrant. The general value is either in the

4th or in the 3rd.. So. cos a is `sqrt(1-12^2/13^2)=5/13` or `+-5/13`.

The given expression is cot a = cos a/sin a and, accordingly, the

answer is given..