General

Another Hard Trig Set

1. If tan^2(alpha)-2tan^2(beta)=1, prove cosine2alpha+sin^2(beta)=0

2. If t=tan(1/2*theta), express the square root of
--->>>>>>>>>>>>(1+sin(theta))(3sin(theta)+4cosine(theta) +5)
in terms of t

3. If sin(3theta)=p and sin^2(theta)=(3/4)-q, prove that p^2+16q^3=12q^2

4. Prove 2cot(1/2)A+tanA=tanAcot^2(1/2)A

5. If 2cosine(3theta)=x+(1/x), show that 2cosine(3theta)=x^3+(1/x)^3

6. If secA-tanA=x, prove then tan(1/2*A)=(1-x)/(1+x)

I forgot why I wrote the following, but I think I wrote these down as hints:

>>>sin3(theta)=3sin(theta)-4sin^3(theta)
>>>cosine3(theta)=4cosine^3(theta)-3cosine(theta)

Btw sorry I couldn't make it neater. And I had to spell out "cosine" fully because the first three letters (which happen to be an abbrevation) are censored.