Prove the identity

Question

________ =sec(x)−tan(x)

Answer 1

cos(-x)/(1-sin(-x) = secx - tanx

try to turn all terms into sines and cosines if nothing else looks promising

cosines are even functions, symmetric about the y axis f(x) = f(-x)

sines are odd functions, symmetric about the origin f(-x) = -f(x)

cosx/(1+sinx) = 1/cosx - sinx/cosx

cosx/(1+sinx) = (1-sinx)/cosx

cos^2(x) = 1-sin^2(x)

1 = sin^2(x)+cos^2(x)

1 = 1 QED