Solve sin &#x2061;<!-- ⁡ --> ( 5 x ) + sin &#x2061;<!-- ⁡ --> ( 3

mikior9t3ue

mikior9t3ue

Answered question

2022-05-11

Solve sin ( 5 x ) + sin ( 3 x ) = cos ( x )

Answer & Explanation

budd99055uruey

budd99055uruey

Beginner2022-05-12Added 16 answers

sin ( 5 x ) + sin ( 3 x ) = = Im ( 2 e i 4 x cos ( x ) ) = 2 sin ( 4 x ) cos ( x )
Hence,
sin ( 5 x ) + sin ( 3 x ) = cos ( x )
can be rewritten in the form
2 ( sin ( 4 x ) 1 2 ) cos ( x ) = 0
which can be rewritten as
( sin ( 4 x ) sin ( π 6 ) ) cos ( x ) = 0
which is easy to solve

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