Simplify the expression: tan(-x)csc(x)

Answer 1

Use some trig identities:

tan(-x) = tan(x)
csc(x) = 1/sin(x)
tan(x) = sin(x)/cos(x)

tan(-x)*csc(x) = tan(x)*(1/sin(x) = (sin(x)/cos(x))*(1/sin(x) = 1/cos(x) = sec(x)