Suppose t is positive. Then inverse cos is an angle in the 1st or 4th quadrant and inverse sine is an angle in the 1st or 2nd quadrant so one will never be the negative of the other. Similar reasoning for when t is negative.
Here's another homework problem from my homework:
There exist angles such that cos (angle) = -sin(angle) (for example, -pi/4 and 3pi/4 are two such angles). However, explain why there do not exist any numbers t such that:
cos^(-1) = -sin^(-1) (t)
or written as
inverse cos (t) = negative inverse sin (t)
Thanks !
Suppose t is positive. Then inverse cos is an angle in the 1st or 4th quadrant and inverse sine is an angle in the 1st or 2nd quadrant so one will never be the negative of the other. Similar reasoning for when t is negative.