Question

evaluate cos[arcsin(-3/5)+arccos(-5/13)

Answer 1

To answer these, you really need to draw a right triangle

I'm going to try to do this:
A
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| \
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B C

Let's use C as our angle, so for arcsin(8/17) that gives us side AB as having length 8 and AC with length 17. Using the Pythagorean theorem, we get the other side to be square root of 289-64 = 15
Then taking the cosine of angle C, we get 15/17
Do a similar thing for the second problem: Using C again, arccos(12/13) gives us side BC with length 12 and AC with length 13, so the other side (AB) is square root of 169-144 = 5.

So csc of C is 13/5.