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Question
Hey I'm Molly i have trouble with proving identities, and
there was a question that i got confused about. It was

sin(x+y)    
--------=   tanx+tany
cosxcosy  

Answer
sin(x + y)/(cos(x)cos(y)) = tan(x) + tan(y)

tan(x) + tan(y) =
(sin(x)/cos(x)) + (sin(y)/cos(y)) =
(sin(x)cos(y) + sin(y)cos(x))/(cos(x)cos(y)) =

this is the same as saying

sin(x + y)/(cos(x)cos(y)) =

or you could have done it this way


(sin(x)cos(y) + sin(y)cos(x))/(cos(x)cos(y)) =
((sin(x)cos(y))/(cos(x)cos(y))) + ((sin(y)cos(x))/(cos(x)cos(y))) =
(sin(x)/cos(x)) + (sin(y)/cos(y)) =
tan(x) + tan(y)

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