1. cos(α° + 70°) = cosα°*cos70° - sinα°*sin70°
3. cos(α + π/3) = cosα*cosπ/3 - sinα*sinπ/3 = cosα*1/2 - sinα*√3/2
5. cos(π/4 + γ) = cosπ/4*cosγ - sinπ/4*sinγ = √2/2(cosγ - sinγ)
7. sin(α + π/4) = sinα*cosπ/4 + cosα*sinπ/4 = √2/2(sinα + cosα)
9. sin (φ - π/2) = sinφ*cosπ/2 - cosφ*sinπ/2 = cosφ
11. cos(φ - 3π/2) = cosφ*cos3π/2 + sinφ*sin3π/2 = -sinφ
13. cos(α - β) = cosα*cosβ + sinα*sinβ
15. sin(β + π/3) = sinβ*cosπ/3 + cosβ*sinπ/3 = sinβ*1/2 + cosβ*√3/2
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Answers & Comments
1. cos(α° + 70°) = cosα°*cos70° - sinα°*sin70°
3. cos(α + π/3) = cosα*cosπ/3 - sinα*sinπ/3 = cosα*1/2 - sinα*√3/2
5. cos(π/4 + γ) = cosπ/4*cosγ - sinπ/4*sinγ = √2/2(cosγ - sinγ)
7. sin(α + π/4) = sinα*cosπ/4 + cosα*sinπ/4 = √2/2(sinα + cosα)
9. sin (φ - π/2) = sinφ*cosπ/2 - cosφ*sinπ/2 = cosφ
11. cos(φ - 3π/2) = cosφ*cos3π/2 + sinφ*sin3π/2 = -sinφ
13. cos(α - β) = cosα*cosβ + sinα*sinβ
15. sin(β + π/3) = sinβ*cosπ/3 + cosβ*sinπ/3 = sinβ*1/2 + cosβ*√3/2