Need Trig Help fast

[speedoman]

Hi, I'm having some difficulty with some trig problems and was hoping someone could help me out fairly quickly.

1. Prove the Identity: tan x/secx -1=csc x + cot x

2. Prove the Identity: 2cos(a + b)sin(a - b)=sin(2a) - sin(2b)

I'm having extra difficulty with these first two. I'm not very good at proving identities.

3. Solve the triangle: c=15, A=78degrees, b=12
I know I need to use the law of cosines to solve this, but i'm not sure how.

7. Compute each of the following by first writing it in trigonometric form. Write you answer in both trigonometric and standard forms.
(a) (6-1i)power of 7

(b) 2+1i/3-3i
i'm totally at a loss on this one

8. Convert the rectangular equation x + y=xy + 2 to a polar equation solve for r

9. Convert the polar equation, cos x - sin y =r

10. Given the points: A(2,-3), B(-5,2), C(1,1) D(0,2) Do the following
(a) Draw vector BA + vector CD in standard position and find its magnitude and direction

(b) Given vector v= 2vectorCB and vector u= vector DA find the angle between vector v and vector u


That's all for now, I would really appreciate any help on this i'm really stuck.

 

[Unco]

Too many, mate.

But, then again, speedos are the way to go so I'll start

1) tan(x)/(sec(x)-1) = csc(x) + cot(x)
If you start with the LHS, getting sec^2(x)-1 as the denominator might help.

2) If you start with the LHS, expanding with compound angle formula and pulling out (sin^2(x)+cos^2(x)) a couple of times may help.

3) a^2 = b^2 + c^2 - 2bc*cos(A)
Here, a=unknown side, b and c are the known sides, and A is the known angle opposite side a.

Show your work.

 

[speedoman]

thanks

Thanks very much for the help. I don't normally like to just ask for the answers to questions like that, but I was seriously frustrated. Your suggestions definitely pointed me on the right track.