F.4 TRIGONOMETRY M2

做這條題目的題目是先將各部份化整為零

cos4θ - 1

=(1 - 2(sin2θ)^2 - 1)

= -2(sin2θ)^2

= -8(sinθ)^2(cosθ)^2

(tanθ)^2 - (cotθ)^2

= [(sinθ)^4 - (cosθ)^4]/[(sinθ)^2(cosθ)^2]

[(tanθ)^2 - (cotθ)^2][cos4θ - 1]

= {[(sinθ)^4 - (cosθ)^4]/[(sinθ)^2(cosθ)^2]} [-8(sinθ)^2(cosθ)^2]

= -8[(sinθ)^4 - (cosθ)^4]

= 8[(cosθ)^4 - (sinθ)^4]

= 8[(cosθ)^2 - (sinθ)^2][(cosθ)^2 + (sinθ)^4]

= 8[(cosθ)^2 - (sinθ)^2]

= 8 cos2θ

2011-03-10 19:20:56 補充：
「做這條題目的策略。」