Simplify (1+sin(t)) / (1+csc(t))

Question

I understand you get on the denominator (1+(1/sin(t))  I don't know how to simplify from there.

 

please help! Thanks!

Answer 1

csct=1/sint

(1+sint)/(1+csct)

1+csct=1+1/sint=(sint+1)/sint  (write 1 as sint/sint and add the two fractions)

(1+sint)/[(sint+1)/sint]

the above is (1+sint) "divided by" (sint+1)/sint

dividing by a number is the same as multiplying by its reciprocal (if you don't see the next step)

(1+sint)*(sint)/(sint+1)

simplify by cancelling the 2 (sint+1)'s

this leaves sin(t) as the answer