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Richardtb 2022-05-23 Answered
Given the function:
f : [ π 2 , π 2 ] R
f ( x ) = cos x cos ( x a ) for some a R
Is it possible to convert it to some kind of translated / otherwise transformed tanx or cotx?
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Answers (2)

Crevani9a
Answered 2022-05-24 Author has 8 answers
Yes it is. You have just to sum ±a in teh argument of the upper cosine
f ( x ) = cos ( x a + a ) cos ( x a )
and use the expression for the sum of angles
f ( x ) = cos ( x a ) cos ( a ) sin ( x a ) sin ( a ) cos ( x a ) = cos ( a ) tan ( x a ) sin ( a )
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res2bfitjq
Answered 2022-05-25 Author has 1 answers
You could also do the following.
f ( x ) = cos x cos ( x a ) = 1 cos ( x a ) c o s ( x ) = 1 cos ( x ) cos ( a ) + sin ( x ) sin ( a ) c o s ( x ) = 1 cos ( a ) + sin ( a ) tan ( x )
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