Rút gọn biểu thức B= 2cosx-3cos(π-x)+5sin(7π/2-x)+cos(3π/2-x)

`B=2cosx-3cos(pi-x)+5sin((7pi)/2-x)+cos((3pi)/2-x)`

`=2cosx+3cos(-x)+5sin[3pi+(pi/2-x)]+cos[pi+(pi/2-x)]`

`=2cosx+3cosx-5sin(pi/2-x)-cos(pi/2-x)`

`=5cosx-5cosx-sinx`

`=-sinx`

`"-----------------------------------------------"`

Công thức đã dùng:

`***` `cos(-x)=cosx`

`***` `cos[(2k+1)pi+x]=-cosx` `(k in ZZ)`

`***` `sin[(2k+1)pi+x]=-sinx` `(k in ZZ)`

`***` `cos(pi/2-x)=sinx`

`***` `sin(pi/2-x)=cosx`