Math Concepts and Examples

Topic:-Trigonometry

Trigonometry is a branch of mathematics that deals with triangles, particularly those plane triangles in which one angle has 90 degrees (right triangles). Trigonometry deals with relationships between the sides and the angles of triangles and with the trigonometric functions, which describe those relationships.

This trigonometry help show us how to solve a problem using Tan formulas.

Question:-

 Solve 

  Cos2x=cosx

Answer:-

Lets write 

cos2x as 2 cos2x-1

So we have 

   2 cos2x-1=cosx

  Then subtract cosx on both sides

2cos2x-1-cosx=cosx-cosx

2cos2x-1-cosx= 0

Lets take cosx as y

So the equaton become

  2y2-y-1= 0

  (y-1)(2y+1)=0

  y-1=0 or 2y+1=0
                 -1
  So y = 1 or y= ------
                  2

Since y=cosx
                    -1
 Cosx=1   or  cosx= ----
                     2
We know that cos0=0 

So cosx=cos0

 x=0 ,

Similarly for the second equation 

 x=120 or 240

For more help on this ,Please reply me.