(3)求函數(shù)y=sinxcosx/(1+sinx+cosx)的值域.
熱心網(wǎng)友
令t=sinx+cosx=√2sin(x+Pi/4)----√2=sinxcosx=(t^2-1)/2因此y=[(t^2-1)/2]/(1+t)=(t-1)/2-√2=-√2-1=-(√2+1)/2=-(√2+1)/2=y∈[-(√2+1)/2,(√2-1)/2][y(√2-2)/4.此時(shí)分母為0]
(3)求函數(shù)y=sinxcosx/(1+sinx+cosx)的值域.
令t=sinx+cosx=√2sin(x+Pi/4)----√2=sinxcosx=(t^2-1)/2因此y=[(t^2-1)/2]/(1+t)=(t-1)/2-√2=-√2-1=-(√2+1)/2=-(√2+1)/2=y∈[-(√2+1)/2,(√2-1)/2][y(√2-2)/4.此時(shí)分母為0]