Question

What does `2sin(arccot(5))-3sin(arc csc(2))` equal?

Answer 1

`2/sqrt26-3/2`

Explanation:

sin arcsin k =k.

If `cot a = x/y, sin a = y/sqrt(x^2+y^2)`.

So, `arc cot (5/1)=arc sin (1/sqrt26)`

If `csc c = d, sin c = 1/d`.

Here x = 5, y = 1, d = 2.
The given expression is
`2 sin arcsin (1/sqrt26)-3 sin arcsin (1/2)`
= `2(1/sqrt26)-3(1/2)`