Given the function: f : [ &#x2212;<!-- − --> &#x03C0;<!-- π --> 2 </

Richardtb

Richardtb

Answered question

2022-05-23

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?

Answer & Explanation

Crevani9a

Crevani9a

Beginner2022-05-24Added 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 )
res2bfitjq

res2bfitjq

Beginner2022-05-25Added 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 )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?