# Some proofs i got stuck on

• Mar 19th 2011, 11:40 PM
chris99191
Some proofs i got stuck on
Prove (sin2x+sinx)/(cos2x+cosx+1)=tanx
I have tried to sub in cos²x+sin²x=1 for 1 and then cancelling but that wouldnt work. I think you need to convert the sinx/cosx into tanx but im still not sure.

Prove (sec-tan)²=(1-sin)/(1+sin)
Another one i got stuck on. I tried to start with the LHS but wasnt sure whether to expand the brackets ot to turn sec into 1/cos and then turn the tan into sin/cos which would make a common denominator. However the ² is still there and I have no idea what to do with that haha

Any help would be appreciated, even just an idea for a start would be good

Thankyou
• Mar 20th 2011, 12:06 AM
Prove It
For the first, you need to use the identities $\displaystyle \sin{2x} \equiv 2\sin{x}\cos{x}$ and $\displaystyle \cos{2x} \equiv 2\cos^2{x} - 1$. See what you can do after you've done that...

For the second, try working on the RHS. Start by multiplying top and bottom of the RHS by $\displaystyle 1 - \sin{\delta}$.