How to prove sec x - tanx sinx= cosx

Answer 1

These are really easy.
Did you notice that for the ones I did for you, I changed everything to sines and cosines ?

LS = secx - tanxsinx
= 1/cosx -(sinx/cosx)sinx
= 1/cosx - sin^2 x/cosx
= (1 - sin^2 x)/cosx
= cos^2 x/cosx
= cosx = RS

Answer 2

for you its easy because you understand it !