Math
posted by mysterychicken on .
1. Find the exact value of 2tan pi/12 / 1tan^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

#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
14cosθ+4cos^3θ = 10+0 = 1
#5. True
sin3θ = sin2θcosθ + cos2θsinθ
= 2sinθcos^2θ + sinθ  2sin^3θ
= 2sinθ  2sin^3θ + sinθ  2sin^3θ
= 3sinθ  4sin^3θ 
Thank you for your constant help! I appreciate it :)