Prove that sin2π6 + cos 2π3 - tan 2π4 = -12.
LHS = sin2π6 + cos 2π3 - tan 2π4
=(12)2+(12)2−12[∵sinπ6=12,cosπ3=12 and tanπ4=1]
=(14+14−1)=−12 = RHS.