Question

prove.

1. (sin 1/2x-cos1/2x)^2= 1-sin x

2. csc x/sec x= 1 + cot x/1 + tan x

Answer 1

For 1) Try expanding and see what you get.
Remember:
"For every angle under the sun, sin^2 + cos^2 is equal to one"
And the double angle formula:
sin 2a = 2sina cosa