Question

How do you evaluate `cot (arcsin(5/6))`?

Answer 1

`sqrt11 /5`

Explanation:

Let arc `sin (5/6)= theta`

`sin theta=5/6`, that means `csc theta =6/5`

`cot^2 theta= csc^2 theta -1= 11/25`

`cot theta= sqrt11 /5`, that means `theta= arc cot (sqrt11 /5)`

Hence `cot arc sin (5/6)= cot arc cot (sqrt11/5)= sqrt11/5`