Question 944893
show that the given equation is an identity; sin(theta+60degrees)-cos(theta+30degrees)=sintheta
***
{{{sin(x+60)-cos(x+30)=sinx}}}
start with left side:
{{{sin(x+60)-cos(x+30)}}}
{{{(sinxcos60+cosxsin60)-(cosxcos30-sinxsin30)}}}
{{{sinx*(1/2)+cosx*(sqrt(3)/2)-(cosx*(sqrt(3)/2)-sinx*(1/2))}}}
{{{sinx*(1/2)+cosx*(sqrt(3)/2)-cosx*(sqrt(3)/2)+sinx*(1/2)}}}
{{{sinx*(1/2)+cosx*(sqrt(3)/2)-cosx*(sqrt(3)/2)+sinx*(1/2)=sinx}}}
verified: left side=right side