Answer to Question #20127 in Trigonometry for Jill

Question

2cos(1/2x)cosx-2sin(1/2x)sinx=1

Answer 1

Using formula for cos of a summ of an angles: cos(a+b)=cosacosb-sinasinb, we've got
2cos(1/2x)cosx-2sin(1/2x)sinx=2cos(1/2x+x)=2cos(3x/2)=1
&
cos(3x/2)=1/2
3x/2=pi/4+2k*pi, where k is integer,& x=pi/6+4k*pi/3
or
3x/2=7pi/4+2k*pi, where k is integer, x=7pi/6+4k*pi/3
Summand 2k*pi is added due to fact that cos is periodic function.