Use a doubleangle formula to simplify the equation sin 2a co

Use a double-angle formula to simplify the equation

Solution

Solution

              Use   a    double   angle   formula   to   simplify the   equation

              sin(2x) + cos(x) = 0

            To find all    solutions    of    the equation that lie    in the interval

             Given Equation   can   be   written as

             2sin(x)cos(x) + cos(x) = 0

             cos(x) [ 2sin(x) + 1 ] = 0

             cos(x) = 0   ,   [ 2 sin(x) + 1 ] =   0

           cos(x) = 0     ,    sin(x) = -1/2

                  x = pi/2    ,    3pi/2

                  x = 7pi/6   ,   11pi/6