Hello ladythugette Originally Posted by

**ladythugette** prove the following identity:

*Secθ- 1/** Sec**θ +1 **≡ Tan² **θ/2* (only the theta is divided by 2)

this is what i've done so far:

**LHS =( secθ- 1)/ (secθ +1)**

** = (1/cos**θ **- 1)** **/(1/cos**θ +1 )

= **1- cosθ/ 1+ cosθ**

**from here, I don't know what to do next. help plz!!! **

You're doing great so far!

Now use$\displaystyle \cos\theta = 1-2\sin^2(\tfrac12\theta)$

on the top, and$\displaystyle \cos\theta = 2 \cos^2(\tfrac12\theta)-1$

on the bottom, and you're there!

Grandad