Question

sin(30°+x)cosx-cos(30°+x)sinx=0,5

Answer 1

sin(30⁰+x)·cosx-cos(30⁰+x)·sinx=0.5;⇒
1/2[sin(30⁰+x-x)+sin(30⁰+x+x)]-1/2[sin(x-30⁰-x)+sin(x+30⁰+x)]=
=1/2[sin30⁰+sin(30⁰+2x)-sin(-30⁰)-sin(30⁰+2x)]=
=1/2(sin30⁰+sin30⁰)=1/2·2sin30⁰=1/2=0.5;