Lesson 48 - Conjugate Rule

Rules:
1) Identity/manipulation
2) sin/cos
3) complex fractions
4) Factor + Cancel
5) combine fractions
6) Conjugate Rule

Prove:    sinx  =  1 + cosx
          1 - cosx      sinx


LS                                   =                                     RS 

    sinx    (1 + cosx)       < multiply by the conjugate           
(1-cosx) (1+ cosx)


 sinx (1+cosx)
 1- cos^2x 

sinx (1+cosx)
  sin^2x

1+ cosx                 =                  1+ cosx
  sinx                                          sinx

Is Cos(x + y) = cosx  + cosy
Cos (12 + 37) = Cos(12) + Cos(37)   < Verify Numerically
        Cos 49 = 0.97 + 0.80
         0.66 = 1.78
  NOT EQUAL!!!

You can proof graphically, algebraically, or numerically.