sin^2X=? cos^2X=?

sin(2x)+cos(2x)=\uff1f

asin\u03b1+bcos\u03b1=\u221a(a²+b²)sin(\u03b1+\u03c6) \u5176\u4e2dtan\u03c6=b/a

sin(2x)+cos(2x)
=\u221a(1²+1²)sin(2x+\u03c6) \uff08\u7531 tan\u03c6=1/1=1\u5f97\u03c6\u53ef\u4ee5\u53d6\u03c6=\u03c0/4\uff09

=\u221a2sin(2x+\u03c0/4)

\u8fd9\u662f\u4e00\u4e2a\u5b9a\u7406\u3002\u4e0d\u7528\u6c42\u3002\u5728\u4e09\u89d2\u5f62\u4e2d\u5206\u4e09\u79cd\u60c5\u51b5\uff0c\u5206\u522b\u4e3a\u76f4\u89d2\u3001\u9510\u89d2\u548c\u949d\u89d2\u3002\u5206\u522b\u7528\u8fb9\u6765\u8868\u793asinX\u548ccosX\uff0c\u7136\u540e\u518d\u5e26\u5165\u5230sin^2X + cos^2X \u4e4b\u4e2d\uff0c\u8fdb\u884c\u5316\u7b80\u5c31\u80fd\u5f97\u5230\u7b49\u5f0f\u53f3\u8fb9\u76841.

sin2x= 2sinx*cosx
cos2x=cos^2x - sin^2x = 2cos^2x -1 = 1- 2sin^2x
另外有一个万能公式：
cos2x= ( 1- tan^2x)/ (1+tan^2x)
sin2x= 2tanx /(1+tan^2x)

sin^2x=2sinx *coxx cos2X=(cosX)^2-(sinX)^2 =2*(cosX)^2-1 =1-2*(sinX)^2

sin2X=2sinXcosX cos2x=2(cosX)^2-1=1-2(sinX)^2

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