Posted by **Anonymous** on Thursday, November 8, 2007 at 9:00pm.

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**, Thursday, November 8, 2007 at 9:35pm
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**, Thursday, November 8, 2007 at 9:47pm
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**, Thursday, November 8, 2007 at 9:50pm
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**, Thursday, November 8, 2007 at 10:00pm
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**, Friday, February 17, 2012 at 5:22pm
secx/sinx - sinx/cosx = cotx

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