Question

What does `sin(arc tan(2))+3cot(arctan(-1))` equal?

Answer 1

`2/sqrt5-3`

Explanation:

If `tan A = 2/1, sin A = 2/sqrt(2^2+1^2)=2/sqrt5`/
If tan B = `-1, cot B = 1/(-1)=-1`.
`sin(arc tan(2)) + 3 cot (arc tan (-1))`
= `sin(arc sin(2/sqrt5)) + 3 cot (arc cot (-1) )`
= `2/sqrt5+3(-1)= 2/sqrt5-3`

IF `O^(-1)` is the inverse of the operator O,
`O(O^(-1))-=O^(-1)(O) -= 1` -

Examples: sin (arc sin x ) = x and `a^(log_a x)` = x.