查詢三角學公式簡化

1.Sin^4θ+sin^2θcos^2θ
=sin^2θ(sin^2θ+cos^2θ)
=sin^2θ

2.√(1-sin^2θ)
=√cos^2θ
=cosθ

3.1.5-1.5sin^2θ
=1.5(1-sin^2θ)
=1.5cos^2θ

4.2-sin^2θ-cos^2θ
=2-(sin^2θ+cos^2θ)
=2-1
=1

5.(1/sin^2θ) -1
=(1-sin^2θ)/sin^2θ
=cos^2θ/sin^2θ
=cot^2θ

6.sinθcos^2θ + sin^3θ-sin^θ
=sinθ(cos^2θ+sin^2θ-1)
=sinθ(1-1)
=0

7.(1-cosθ)/sinθ + sinθ/(1-cosθ)
=(1-2cosθ+cos^2θ+sin^2θ)/[sinθ(1-cosθ)]
=(1-2cosθ+1)/[sinθ(1-cosθ)]
=2(1-cosθ)/[sinθ(1-cosθ)]
=2/sinθ
=2cscθ

2007-03-27 20:32:53 補充：
used:sin^2θ cos^2θ=1

2007-03-27 20:33:13 補充：
sin^2θ＋cos^2θ=1

sin^4Θ+sin^2Θcos^2Θ

=sin^2Θ(sin^2Θ+1×cos^2Θ) <-----抽 sin^2Θ

=sin^2Θ(sin^2Θ+cos^2Θ) <-----恆等式, sin^2Θ+cos^2Θ =1

=sin^2Θ(1)

=sin^2Θ//