Posted by Anonymous on .
Prove:
sinx + tanx = tanx (1 + cosx)
What I have so far:
LS:
= sinx + tanx
= sinx + (sinx / cosx)
= (sinx) (cosx) + sinx / cos
= tanx (cosx + sinx)
I don't know what to do now

Mathematics  Trigonometric Identities 
Reiny,
Your second last line needs brackets, and the following line makes no sense
Why not work on the right side?
RS = tanx(1+cosx)
=tanx + tanxcosx after expanding
= tanx + (sinx/cosx)cosx
= tanx + sinx
= LS 
Mathematics  Trigonometric Identities 
Anonymous,
My second last line:
(sinx) (cosx) + sinx
_________________________
cosx
When I did the right side, I get the same problem as the left side:
RS:
= tanx + (1 + cosx)
= (sinx / cosx) (1 + cosx)
= (1 + cosx) (cosx)
= (sinx) (1 + cosx)
_______________________
cosx
= (sinx) + (cosx)(sinx)
________________________
cosx
And ... my teacher wants everything in terms of cos and sin 
Mathematics  Trigonometric Identities 
Anonymous,
RS = tanx(1+cosx)
=tanx + tanxcosx after expanding
= tanx + (sinx/cosx)cosx
= tanx + sinx
= LS
For this line "=tanx + tanxcosx after expanding", how did you get the second tanx from and what has happened to the addition sign? 
Mathematics  Trigonometric Identities 
Reiny,
from you second last line
(sinx) (cosx) + sinx
_________________________
cosx
= sinx[cosx + 1]/cosx , ....I took out a common factor
= tanx(cosx + 1)
= RS
You said "And ... my teacher wants everything in terms of cos and sin"
your teacher probably suggested changing everything to sines and cosines as you work your way through. Notice that is also what I did as I showed the steps.
I would never have restricted my students to use only a part of their trig knowledge, why not make use of all the relationships at your hand, picking the simplest way? 
Mathematics  Trigonometric Identities 
Kay,
secx/sinx  sinx/cosx = cotx