Question

PROVE THAT
cos+sin / cos-sin =1+tan / 1-tan

Answer 1

Answer:

Step-by-step explanation:

LHS

= cosA/1-(sinA/cosA) + sinA/1-(cosA/sinA)

=cosA/(cosA-sinA)/cosA+sinA/(sinA-cosA)/sinA

=cosA ×cosA/cosA-sinA+(sinA×sinA)/sinA-cosA

=cos^2 A/cosA-sinA + sin^2 A/sinA-cosA

=cos^2 A-sin^2 A/cosA-sinA

=(cosA+sinA) (cosA-sinA)/cosA-sinA

=cosA+sinA