Question

how do i solve

tan(165)

and

sin(285)

Answer 1

the instructions probably say:
evaluate the exact value of ....
that means, you do not use a calculator.
(That does not mean we cannot use one to check the answer we find)

the trick for all of these is to split the given angle into two or more parts whose trig values we know
so tan(165) = tan(90+75) or tan(180-15) or ...

let's use tan(180-15)
= -tan 15 , (I know that from my CAST properties)

now we have to find tan 15
tan(15)
= tan(45-30)
= (tan45 - tan30)/(1 + tan45tan30)
= (1 - 1/√3)/(1 + 1/√3)
= (√3 - 1)/(√3 + 1)

then
tan165
= -tan15 = (1 - √3)/(√3 + 1)

for the second one, sin285,
I would use sin(360-75)
= - sin75

then use 45 and 30 and the sin(A+B) expansion.
check your answer with your calculator,
I did my first result, and I am right.