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1. Find the complete exact...

1. Find the complete exact solution of sin x = −√3/2.

2. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places.

3. Solve tan² x + tan x – 1 = 0 for the principal value(s) to two decimal places.

4. Prove that tan² α – 1 + cos² α = tan² α sin² α.

5. Prove that tan β sin β + cos β = sec β.

6. Prove that tan λ cos² λ + sin² λ/sin λ = cos λ + sin λ.

7. Prove that 1 + tanθ/1 - tanθ = sec²θ + 2tanθ/1 - tan²θ.

8. Prove that sin² ω - cos² ω/tan ω sin ω + cos ω tan ω = cos ω – cot ω cos ω.

9. Find a counterexample to shows that the equation sec α – cos α = sin α sec α is not

an identity.

10. Write tan (╥/4 - β) as a function of β only.

11. Write cos (λ + ╥/3) as a function of λ only.

12. Write cos(–83°) as a function of a positive angle.

13. Write sin(125°) in terms of its cofunction. Make sure your answer is a function

of a positive angle.

14. Find the exact value of sin(195°).

15. Sketch a graph of y = sin(–2x), paying particular attention to the critical points.

16. If cot 2θ = 5/12 with 0 ≤ 2θ ≤ ╥, find cosθ, sinθ, and tanθ.

17. Find the exact value of sin2α if cosα = 4/5 (α in Quadrant I).

18. Find the exact value of tan2β if sinβ = 5/13 (β in Quadrant II).

19. Solve sin 2x + sin x = 0 for 0 ≤ x ≤ 2╥.

20. Write 2sin37°sin26° as a sum (or difference).

i need the answers and the work i can give $10.

2. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places.

3. Solve tan² x + tan x – 1 = 0 for the principal value(s) to two decimal places.

4. Prove that tan² α – 1 + cos² α = tan² α sin² α.

5. Prove that tan β sin β + cos β = sec β.

6. Prove that tan λ cos² λ + sin² λ/sin λ = cos λ + sin λ.

7. Prove that 1 + tanθ/1 - tanθ = sec²θ + 2tanθ/1 - tan²θ.

8. Prove that sin² ω - cos² ω/tan ω sin ω + cos ω tan ω = cos ω – cot ω cos ω.

9. Find a counterexample to shows that the equation sec α – cos α = sin α sec α is not

an identity.

10. Write tan (╥/4 - β) as a function of β only.

11. Write cos (λ + ╥/3) as a function of λ only.

12. Write cos(–83°) as a function of a positive angle.

13. Write sin(125°) in terms of its cofunction. Make sure your answer is a function

of a positive angle.

14. Find the exact value of sin(195°).

15. Sketch a graph of y = sin(–2x), paying particular attention to the critical points.

16. If cot 2θ = 5/12 with 0 ≤ 2θ ≤ ╥, find cosθ, sinθ, and tanθ.

17. Find the exact value of sin2α if cosα = 4/5 (α in Quadrant I).

18. Find the exact value of tan2β if sinβ = 5/13 (β in Quadrant II).

19. Solve sin 2x + sin x = 0 for 0 ≤ x ≤ 2╥.

20. Write 2sin37°sin26° as a sum (or difference).

i need the answers and the work i can give $10.

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