![已知tan(π4+a)=12求cos2asin2a+cos²a,第1張 已知tan(π4+a)=12求cos2asin2a+cos²a,第1張](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
已知tan(π/4 a)=1/2
求cos2a/sin2a cos²a網友廻答:
- 已知,tan(π/4 a) = [1 tan(a)]/[1-tan(a)] = 1/2 ,可得:tan(a) = -1/3 ;
tan(2a) = 2tan(a)/[1-tan^2(a)] = -3/4 ,
sec^2(a) = 1 tan^2(a) = 10/9 ,
cos^2(a) = 1/sec^2(a) = 9/10 ;
所以,cos(2a)/sin(2a) cos^2(a) = 1/tan(2a) cos^2(a) = -4/3 9/10 = -13/30 。
網友廻答:
- tanπ/4=1所以(1 tana)/(1-tana)=1/22 2tana=1-tanatana=-1/3sina/cosa=tana=-1/3cosa=-3sina則cos²a=9sin²a因爲sin²a cos²a=1所以sin²a=1/10,cos²a=9/10cos2a=cos²a-sin²a...
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