Question

Prove the identity.
1/cosx-cosx/1+sinx=tanx

Answer 1

Answer:

Step-by-step explanation:

Please see the attached picture.

Answer 2

Step-by-step explanation:

(1/cosx)-[cosx/(1+sinx)]

cross multiplication,

=(1+sinx-cos^2x)/[cosx(1+sinx)]

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

=[sin^2x+cos^2x+sinx-cos^2x)/[(cosx(1+sinx)]

=(sin^2x+sinx)/[cosx(1+sinx)]

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

=sinx/cosx

=tanx