化简sin×[a+(2n+1)π]+2sin×[a-(2n+1)π]/sin(a-2nπ)coS(2nπ-a) (n属于Z)

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化简sin×[a+(2n+1)π]+2sin×[a-(2n+1)π]/sin(a-2nπ)coS(2nπ-a) (n属于Z)

化简sin×[a+(2n+1)π]+2sin×[a-(2n+1)π]/sin(a-2nπ)coS(2nπ-a) (n属于Z)
化简sin×[a+(2n+1)π]+2sin×[a-(2n+1)π]/sin(a-2nπ)coS(2nπ-a) (n属于Z)

化简sin×[a+(2n+1)π]+2sin×[a-(2n+1)π]/sin(a-2nπ)coS(2nπ-a) (n属于Z)
因为n属于Z,所以2n+1为奇数,所以sin[a+(2n+1)π]=sin(a+π)=-sina,sin[a-(2n+1)π]=sin(a-π)=-sina
所以分子为sin【a+(2n+1)π】+2sin【a-(2n+1)π】=-sina-2sina=-3sina
因为2n是偶数,所以sin(a-2nπ)=sina,cos(2nπ-a)=cos(-a)=cosa,分母即sinacosa
所以-3sina/sinacosa=-3/cosa

sin×[a+(2n+1)π]+2sin×[a-(2n+1)π]/sin(a-2nπ)coS(2nπ-a) =sin×[a+π]+2sin×[a-π]/sina coS(-a) =-sina+(-2sina)/sina cosa =cos a-sina

2n是偶数,2n+1为奇数,sin×[a+(2n+1)π]+2sin×[a-(2n+1)π]/sin(a-2nπ)coS(2nπ-a)=-3sina/sinacosa=-3/cosa