The greatest value of sin3x+cos3x is
1
2
3
The explanation for the correct answer.
Find the greatest value:
y=sin3x+cos3xdydx=3sin2xcosx-3cos2xsinxdydx=3sinxcosx(sinx-cosx)Putdydx=03sinxcosx(sinx-cosx)=0x=0,Ï€2,Ï€4
y has a maximum value at x=0orπ2.
ymax=1
Hence, option A is the correct answer.