簡化sin4次X+cos2X+sin2次Xcos2次X 關於sin cos tan 有什麼公式?

2017-05-27 4:45 pm

回答 (3)

2017-05-27 5:06 pm
✔ 最佳答案
(sinx)^4+cos2x+(sinx)^2*(cosx)^2
=(sinx)^2*((sinx)^2+(cosx)^2)+cos2x
=(sinx)^2+cos2x
=(sinx)^2+1-2(sinx)^2
=1-(sinx)^2
=(cosx)^2

用了公式:
(sinx)^2+(cosx)^2=1
cos2x=1-2(sinx)^2
2017-05-27 6:17 pm
1
Sol
Sin^4 x+Cos2x+Sin^2 xCos^2 x
=Sin^4 x+(1-2Sin^2 x)+Sin^2 x(1-Sin^2 x)
=Sin^4 x+1-2Sin^2 x+Sin^2 x-Sin^4 x
=1-Sin^2 x
=Cos^2 x
2
Sin^4 θ+Cos^2 θ+Sin^2 θCos^2 θ
=Sin^4 θ+(1-Sin^2 θ)+Sin^2 θ(1-Sin^2 θ)
=sin^4 θ+1-Sin^2 θ+Sin^2 θ-Sin^4 θ
=1
2017-05-27 5:18 pm
可以用 〖sin〗^2 x+〖cos〗^2 x = 1
其實把所有 sin ^2 x 變成 (1 - cos ^2 x ) ,你就可以解決這條問題了。


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