Question

1. Find the exact value of 2tan pi/12 / 1-tan^2 pi/12
root 3/3?

2. Given tanθ = -1/3 and with θ in quadrant IV, find the exact value of cos2(θ)
4/5

3. Exact value of cos^2 67.5 - sin^2 67.5
root3 /2

4. The expression cos 3θ can be rewritten as 1 - 4cosθ + 4cos^3θ
False

5. The expression sin 3θ can be rewritten as 3sinθ - 4sin^3 θ
Not sure

Answer 1

#1. ok

#2. find sinθ and cosθ and let 'er rip

#3. you have cos 135° = -1/√2
cos2θ = cos^2 θ - sin^2 θ

#4. Obviously false, since if θ=90 we have
cos3θ = 0
1-4cosθ+4cos^3θ = 1-0+0 = 1

#5. True
sin3θ = sin2θcosθ + cos2θsinθ
= 2sinθcos^2θ + sinθ - 2sin^3θ
= 2sinθ - 2sin^3θ + sinθ - 2sin^3θ
= 3sinθ - 4sin^3θ

Answer 2

Thank you for your constant help! I appreciate it :)