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Jasmin Pineda

Jasmin Pineda

Answered question

2022-06-15

Given equation:
sin ( x ) + sin ( 5 x ) sin ( 3 x ) cos ( x ) + cos ( 5 x ) cos ( 3 x ) = tan ( 3 x ) ,
what is the easiest way to solve it?

Answer & Explanation

Misael Li

Misael Li

Beginner2022-06-16Added 14 answers

Hint:
Simply write
sin x + sin 5 x = sin ( 3 x 2 x ) + sin ( 3 x + 2 x ) = 2 sin 3 x cos 2 x
and similarly fot cos x + cos 5 x
Hector Petersen

Hector Petersen

Beginner2022-06-17Added 6 answers

2 sin ( x + 5 x 2 ) cos ( x 5 x 2 ) sin ( 3 x ) 2 cos ( x + 5 x 2 ) cos ( x 5 x 2 ) cos ( 3 x ) = sin ( 3 x ) ( 2 cos 2 x 1 ) cos ( 3 x ) ( 2 cos 2 x 1 ) = tan ( 3 x )

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