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.

For determining the length of the chords in Circle, Rectangular Co ordinate System is used. According the graphical representation, radius towards right side is positive and towards left is negative.

Topic : Length of Chords in a Circle of radius r

Using definite integrals we can calculate the length of chords with some constraints.

Question : In a circle of radius r, find the average length of the chords perpendicular to the diameter [-r, r].

Solution :

For more information and clarification related to the above topic you can find help at calculus help.

Topic : Integration

Question : Integrate e^1/x / x²

Solution :  

Topic : Integration

Question : Integrate   ∫ (2+3Sin³ x)/ Sin² x dx

Solution :