pembuktian identitas trigonometri

IDENTITAS TRIGONOMETRI

                                                                                                                                            

      Y

                                           

                           r                                            y

                     β 

  O                      x                                     X

              

      •     Sin β =  

           y     =  r sin β…………..(1)

·         Cos  β =

               x     = r cos β…………..(2)

      

       •   Tan β = …………….……….(3)

1.Tan β =

    Tan β =

    Tan β =

     Tan β =

     Cot β =

2.sin²β + cos²β = 1

=   x²  +  y²  =  r²

 =  (r sin β)²  +  (r cosβ)²   = r²

 =   r² sin² β  +    r² cos² β  = r²   : r²

         sin²β  +   cos²β       = 1

3. 1 + Tan² β = sec² β

cos² β + sin² β  =  1

                                 cos² β

1 +    = 

1 + Tan² β  = Sec² β

4.1 +  Cot² β   = csc² β

cos² β + sin² β  =  1

                                 sin² β

     + 1 = 

Cot² β + 1  = Csc² β

1 +  Cot² β  = Csc² β