Posted by Matt on .
Prove (1+secx)/(tanx+sinx)=cscx

trig 
MathGuru,
Let's use a few identities:
secx = 1/cosx
tanx = sinx/cosx
cscx = 1/sinx
Therefore:
(1 + 1/cosx)
 = cscx
(sinx/cosx + sinx)
Change 1 in the numerator to cosx/cosx, which is the equivalent of 1. Also, multiply sinx in the denominator by cosx/cosx.
(cosx/cosx + 1/cosx)
 = cscx
(sinx/cosx + sinx(cosx)/cosx)
(cosx + 1)/cosx
 = cscx
[sinx + sinx(cosx)]/cosx
(cosx + 1)/[sinx + sinx(cosx)] = cscx
(cosx + 1)/sinx(cosx + 1) = cscx
1/sinx = cscx
cscx = cscx
I hope this helps.