| cos5θ,cos6θ,cos7θの導出例
cos2θ=2(cosθ)^2-1
cos4θ=2(cos2θ)^2-1=2{2(cosθ)^2-1}^2-1=8(cosθ)^4-8(cosθ)^2+1
sin2θ=2sinθcosθ
sin4θ=2sin2θcos2θ=2(2sinθcosθ){2(cosθ)^2-1}={8(cosθ)^3-4cosθ}sinθ
cos5θ=cos4θcosθ-sin4θsinθ
={8(cosθ)^4-8(cosθ)^2+1}cosθ-{8(cosθ)^3-4cosθ}sinθ・sinθ
={8(cosθ)^4-8(cosθ)^2+1}cosθ-{8(cosθ)^3-4cosθ}{1-(cosθ)^2}
=16(cosθ)^5-20(cosθ)^3+5cosθ
sin5θ=sin4θcosθ+cos4θsinθ
={8(cosθ)^3-4cosθ}sinθ・cosθ+{8(cosθ)^4-8(cosθ)^2+1}・sinθ
={16(cosθ)^4-12(cosθ)^2+1}sinθ
cos6θ=cos5θcosθ-sin5θsinθ
={16(cosθ)^5-20(cosθ)^3+5cosθ}cosθ-{16(cosθ)^4-12(cosθ)^2+1}sinθ・sinθ
={16(cosθ)^5-20(cosθ)^3+5cosθ}cosθ-{16(cosθ)^4-12(cosθ)^2+1}{1-(cosθ)^2}
=32(cosθ)^6-48(cosθ)^4+18(cosθ)^2-1
sin6θ=sin5θcosθ+cos5θsinθ
={16(cosθ)^4-12(cosθ)^2+1}sinθ・cosθ+{16(cosθ)^5-20(cosθ)^3+5cosθ}sinθ
={32(cosθ)^5-32(cosθ)^3+6cosθ}sinθ
cos7θ=cos6θcosθ-sin6θsinθ
={32(cosθ)^6-48(cosθ)^4+18(cosθ)^2-1}cosθ
-{32(cosθ)^5-32(cosθ)^3+6cosθ}sinθ・sinθ
={32(cosθ)^6-48(cosθ)^4+18(cosθ)^2-1}cosθ
-{32(cosθ)^5-32(cosθ)^3+6cosθ}{1-(cosθ)^2}
=64(cosθ)^7-112(cosθ)^5+56(cosθ)^3-7cosθ
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No.89138 - 2024/10/16(Wed) 02:17:33 |
