Find the exact value nbspsin-1sin-9pi8 find the exact value

Question

1. Find the exact value:  sin^-1[sin(-9π/8)]

2. Find the exact value: sin^-1(cos(3π/4))

3. Establish the identity: (cot θ/1-tan θ) + (tan θ/1 - cot θ) = 1 + tan θ + cot θ

4. Find the exact value of: tan(sin^-1(3/5)+(π/6))

5. Establish the identity:  sin(α+β)/sin(α-β) = tan α + tan β/tan α - tan β

6. Find the exact value of:  csc(7π/8)

7. Establish the identity:  tan v/2 = csc v - cot v

8. Establish the identity:  sin(4θ) - sin(8θ)/cos(4θ) - cos(8θ) = -cot(6θ)

9. Solve the equation. Give general formula for all the solutions. List six solutions.

tan θ/2 = -1  

10. Solve on the interval 0 ≤ θ < 2π:

3(1 - cos θ) = sin²θ

11. If tan α = x + 1 and tan β = x - 1, show that 2cot(α - β) = x².