# Question 6c606

Jan 15, 2018

#### Explanation:

color(red)((1+sinA)/cosA+cosB/(1-sinB)

=color(green)({cos (A/2)+sin(A/2)}^2/{cos^2(A/2)-sin^2(A/2)}+{cos^2(B/2)-sin^2(B/2)}/{cos(B/2)-sin(B/2)}^2

=color(red)((cos(A/2)+sin(A/2))/{cos(A/2)-sin(A/2)}+(cos(B/2)+sin(B/2))/(cos(B/2)-sin(B/2))

=color(green)([{(cos(A/2)+sin(A/2))cdot(cos(B/2)-sin(B/2))}+{(cos(B/2)+sin(B/2))cdot(cos(A/2)-sin(A/2))}]/{(cos(A/2)-sin(A/2))cdot(cos(B/2)-sin(B/2))}

=color(red)({cos(A/2) cdot cos(B/2)-cos(A/2) cdot sin(B/2)+cos(B/2) cdot sin(A/2)-sin(A/2) cdot sin(B/2)+cos(B/2)cos(A/2)-cos(B/2) cdot sin(A/2)+sin(B/2) cdot cos(A/2)-sin(B/2) cdot sin(A/2)}/{cos(A/2)cos(B/2)-cos(A/2) cdot sin(B/2)-sin(A/2) cdot cos(B/2)+sin(A/2) cdot sin(B/2)}

=color(green)((2{cos(A/2)cdot cos(B/2)-sin(A/2) cdot sin(B/2)})/({cos(A/2)cdot cos(B/2)+sin(A/2) cdot sin(B/2)}-{sin(A/2)cos(B/2)+cos(A/2)sin(B/2)}

=color(red)((2 cos((A+B)/2))/{cos((A-B)/2)-sin((A+B)/2)}

=color(green)((2 cos((A+B)/2)cdot2sin((A-B)/2))/{2 cdot cos((A-B)/2) cdot sin((A-B)/2)-2 cdot sin((A+B)/2)cdot sin((A-B)/2)

=color(red)((2(sinA-sinB))/(sin(A-B)+cosA-cosB)#

Hope it helps...
Thank you...