Simplify (cos x)/(sec(x) + 1)

Question

a. cot^2 x - cot^2 x * cos x
b. cot^2 x + cot^2 x * cos x
c. cos^2 x + cos x
d. cot^2 x - cot^2 x * sin x

Answer 1

multiply top and bottom by secx - 1 and you have
cosx(secx-1)/(sec^2x-1)
= cosx(secx-1)/tan^2x
= (1-cosx)/tan^2x
see what you can make of that
Not sure it's any "simpler" though