Question

secx+sinx(-tanx)=cosx prove

Answer 1

1/cos(x) + sinx(-sin/cos) = cosx
You have a common denominator so you have
(1 - sin^2x)/cosx = cosx
1 - sin^2x = cos^2x by the sin^2x + cos^2x = 1 identity
cos^2x/cosx = cosx

cosx = cosx

Answer 2

secx= 1/cosx

tanx=sinx/cosx

plug them into your equation you have

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

Answer 3

SORRY "+" instead of "="