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tilfaen4a

tilfaen4a

Answered question

2022-05-19

Deduce tan ( π x ) = tan x

Answer & Explanation

Michaela Alvarado

Michaela Alvarado

Beginner2022-05-20Added 11 answers

Since sin ( π ) = 0 , cos ( π ) = 1 you have
tan ( π x ) = sin ( π x ) cos ( π x ) = sin ( π ) cos ( x ) sin ( x ) cos ( π ) cos ( π ) cos ( x ) + sin ( π ) sin ( x ) = + sin ( x ) cos ( x ) = sin ( x ) cos ( x ) = tan ( x )
shelohz0

shelohz0

Beginner2022-05-21Added 3 answers

Hint
tan ( A B ) = tan A tan B 1 + tan A tan B . Use A = π and B=x
So tan π tan x 1 + tan π tan x = tan x . (Since tan π = 0).
So tan ( π x ) = tan x (proved)

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