Question 88275
{{{sin(x-3*pi/2)=cos(x)}}}




{{{sin(x)cos(3pi/2)-cos(x)sin(3pi/2)=cos(x)}}} Use the trig identity {{{sin(A-B)=sin(A)cos(B)-cos(A)sin(B)}}}


{{{sin(x)cos(3pi/2)-cos(x)(-1)=cos(x)}}} Evaluate {{{sin(3pi/2)}}} to get -1



{{{sin(x)(0)-cos(x)(-1)=cos(x)}}} Evaluate {{{cos(3pi/2)}}} to get 0



{{{cos(x)=cos(x)}}} Multiply. So the identity has been proven


As always we can graph the two expressions (the given and the result) to see if they are equivalent.