Simplify each expression using the fundamental identities.

Question

1. Sec x csc x / sec^2x+csc^2x
2. Sec x + tan x / sec x + tan x - cos x

Answer 1

sin^2+cos^2 = 1, so

sec^2 + csc^2 = 1/cos^2 + 1/sin^2
= (sin^2+cos^2)/(sin^2 cos^2)
= 1/(sin^2 cos^2)
= sec^2 csc^2
so,

(sec csc) / (sec^2 csc^2)
= 1/(sec csc)
= sin cos
= 1/2 sin(2x)

#2 is missing too many parentheses to work on it. That dangling cos x bothers me.