Question

cos2x+cosx=0 求sin2x+sinx的值

Answer 1

cos2x+cosx=2cos²x-1+cosx=0

(cosx+1)(2cosx-1)=0

cosx=-1,cosx=1/2

cosx=-1

则x=2kπ+π

2x=4kπ+2π

所以sin2x+sinx=0+0=0

cosx=1/2

x=2kπ+π/3,x=2kπ-π/3

2x=4kπ+2π/3,2x=4kπ-2π/3

所以sin2x+sinx=√3/2+√3/2=√3

或sin2x+sinx=-√3/2-√3/2=-√3

所以sin2x+sinx=0或√3或-√3