How do you simplify this expression 1+tgx/sinx+cosx?

1 Answer
Mar 31, 2018

#(1+tanx)/(sinx+cosx)=secx#

Explanation:

.

#(1+tanx)/(sinx+cosx)#

Let's multiply both the numerator and the denominator by #secx#:

#(secx(1+tanx))/(secx(sinx+cosx))=(secx(1+tanx))/(1/cosx(sinx+cosx))=#

#(secx(1+tanx))/(sinx/cosx+cosx/cosx)=(secx(1+tanx))/(tanx+1)=#

#=(secx(1+tanx))/(1+tanx)=(secxcancelcolor(red)((1+tanx)))/cancelcolor(red)((1+tanx))=secx#