I have a few trig problems that im stuck on, and I cant figure them out. Can someone please help me and explain how you solved them? You dont need to solve all of them if you dont want to but every answer and explaination helps greatly!!! Every * represents a subquestion.

1. Prove the identity: 2sec^2(theta)tan^2(theta)-tan^4(theta)=sec^4(theta)-1.
*Factor the left side of the identity:
*Use a pythagorean identity to rewrite in terms of sec and simplify. Do not multiply.
*To make both identities equal use which identity?

2. Using terms of Pi find all solutions for 4sec(x)tan(x)-4sec(x)+tan(x)-1=0 on [0,2pi)

3. Using terms of Pi find all solutions for cos2x-sqrt(3)sin(x)=1 on [0,2pi)

4. Find the function value of sin(9pi) using coordinates on the unit circle

5. Assume that d>0, 0<theta<pi/2, then find the expressions for the indicated trig functions. Let x=dcos(theta) in Sqrt(d^2-x^2) Then find Sin(theta) and Cos(theta)

6.Factor and simplify cos^3(x)+8

7. Solve finding all solutions of tan(x)= -(sqrt(3)/3)
x=___+pi*k, where k is any intereger. Write in terms of pi