Number of solutions of the equation tanx+secx=2cosx  in [0,2π]  is

1+sinxcosx=2cosx 1+sinx=2−2sin2x2sin2x+sinx−1=0(1+sinx)(2sinx−1)=0sinx=−1, sinx=12sinx=−1⇒x=3π2  for which does not satisfy the equation and sinx=12⇒x=π6,5π6∴  Required number of solution is 2