Lesson Truly elegant solution to one trigonometric equation

Truly elegant solution to one trigonometric equation

Problem 1

     -  = 1.


Multiply both sides by .

     -  = .


It can be written in this form

     -  = .


Use the formula of adding arguments for sine

     = .


It may happen in one of the two cases


Case 1.   = .

          which implies  = 0,

or

Case 2.   =  - ,

         which implies   =  =  = -.

         Since we consider the angles in the interval [0,2pi), it is equivalent to   = .


So, we get the ANSWER :  The given equation has two solutions in the interval [0,2pi)

                         a)   = 0,   and  b)   = .