verify 2cos^2?-sin^2?+1÷cos?=3cos?

Question

Steps On How To Verify The Identity 

Answer 1

Rocio,

 

Recall the identity sin² (Θ) + cos² (Θ) =1 and so sin² (Θ) = 1 - cos² (Θ).

 

Then in  [2 cos² (Θ) - sin² (Θ) + 1]/cos (Θ)  = 3 cos (Θ)   substitute for the sin2 (Θ) 

 

[2 cos2 (Θ) - (1 - cos² (Θ)) + 1]/cos (Θ) = 3 cos (Θ)

 

[2 cos2 (Θ) + cos2 (Θ)]/cos (Θ) = 3 cos (Θ)  , and dividing thru by the cosine

 

[2 cos (Θ) + cos (Θ)] = 3 cos (Θ)