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verify that equation is an identity:

1. sin(A+π) = -sinA

2. tan(x+45) = (1 + tanx) / (1 - tanx)

Guest May 19, 2018
#1
+93633
+1

verify that equation is an identity:

It depends on what you are allowed to use to verify it.... but..

1. sin(A+π) = -sinA

$$LHS=sin(A+\pi)\\ LHS=sinAcos\pi+cosAsin\pi \\ LHS=(sinA*-1)+(cosA*0)\\ LHS=-sinA\\ LHS=RHS\\ QED$$

2. tan(x+45) = (1 + tanx) / (1 - tanx)

$$LHS\\ =tan(x+45)\\ =\frac{tanx+tan45}{1-tanxtan45}\\ =\frac{tanx+1}{1-tanx}\\ =\frac{1+tanx}{1-tanx}\\ =RHS\\ QED$$

Melody  May 19, 2018