How do you simplify the expression $cot(arcsin (-7/13))$ ?

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Answer 1 · 2016-06-24T17:12:39

$-sqrt 120/7$ against principal value of arc sin (-7/13), in the 4th quadrant. Of course, the general solution is $+-sqrt120/7$ .

Let $a = arc sin (-7/13)$ . Then, $sin a = -7/13<0$ .

a is in either 3rd quadrant or in the fourth. The principal value is in

4th. Accordingly,

$cos a = sqrt(1-7^2/13^2)=sqrt 120/13$ , against principal a.

Also, for the 3rd quadrant a, $cos a=-sqrt120/13$ .

The given expression is

$cot a =cos a/sin a=- sqrt120/7$ , against principal a and

$sqrt120/7$ , for the other a.

How do you simplify the expression cot(arcsin (-7/13))cot(arcsin (-7/13))?