Are these two equation equal? f(x)=sin(4x)−sin(3x)cos(x) and g(x)=sin(x)cos(3x)

Jacoby Erickson

Jacoby Erickson

Answered question

2022-10-28

Are these two equation equal? f ( x ) = sin ( 4 x ) sin ( 3 x ) cos ( x ) and g ( x ) = sin ( x ) cos ( 3 x )

Answer & Explanation

Messiah Trevino

Messiah Trevino

Beginner2022-10-29Added 18 answers

The identity in question is
sin ( a + b ) = sin ( a ) cos ( b ) + sin ( b ) cos ( a )
and so
sin ( 3 x ) cos ( x ) + sin ( x ) cos ( 3 x ) = sin ( 3 x + x ) = sin ( 4 x ) sin ( 4 x ) sin ( 3 x ) cos ( x ) = sin ( x ) cos ( 3 x )
so yes, f ( x ) = g ( x )

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