Question

16) Please help with this question. Please answer with normal text (Ex: pi/4,etc... not math settings).

Answer 1

We can use tan(x) = sin(x)/cos(x). Plug in numbers to get:
tan(x+pi/2) = sin(x+pi/2)/cos(x+pi/2) 

Here, you can use the sin and cos addition identity:
tan(x+pi/2) = (sin(x)cos(pi/2)+cos(x)sin(pi/2))/(cos(x)cos(pi/2)+sin(x)sin(pi/2))

If you simplify this, you get:
0+cos(x)/0-sin(x) 

Which is the definition of cot(x). But, we can't forget about the '-' sign, so, the answer is -cot(x)