Answer:
csc(q)
Step-by-step explanation:
You could plug in values for q for the problem and the choices and see which choice gives the same outputs. Of course, that would mean you need to know that cot() is cos()/sin() or 1/tan() and csc()=1/sin()
So anyways you can also use identities to rewrite the given expression
sin(q)+cos(q)cot(q) [given ]
sin(q)+cos(q)cos(q)/sin(q) by quotient identity
sin(q)+cos^2(q)/sin(q) [simplify]
sin(q)sin(q)/sin(q)+cos^2(q)/sin(q) multiply first term by 1
sin^2(q)/sin(q)+cos^2(q)/sin(q) [simplify ]
(sin^2(q)+cos^2(q))/sin(q) [combined fractions ]
1/sin(q) by Pythagorean identity
csc(q) by reciprocal identity
