A student found the exact value of cos 30 degrees using the fact that 30 degrees = 60 degrees minus 30 degrees and got zero. What was his error? What do you think he did wrong?

let A=60 degrees B=30 degrees   we know that cos (A-B)=cos A*cos B+sinA*sinB so cos (60-30)=cos60*cos30+sin60*sin30-- > (1/2)*( √3/2)+( √3/2)*(1/2)--- > √3/4+ √3/4---- > √3/2 so cos (60-30)= √3/2 the  mistake is that the student used the formula for the cosine of the difference: cos ( A-B) but confused the sign, and use - instead of +
getting the wrong value. cos (60-30)=cos60*cos30-sin60*sin30----- > √3/4- √3/4---- > 0---- > wrong value obtained by the student