Is sin(5x)-sin(x)=2cos(3x)sin(2x) ?

The answer to whether sin(5x)-sin(x)=2cos(3x)sin(2x) is True

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prove sin(5x)-sin(x)=2cos(3x)sin(2x)

prove

sin (5 x) - sin (x) = 2 cos (3 x) sin (2 x)

True

Solution steps

sin (5 x) - sin (x) = 2 cos (3 x) sin (2 x)

Manipulating left side

sin (5 x) - sin (x)

Rewrite using trig identities

= 2 sin (2 x) cos (3 x)

= 2 cos (3 x) sin (2 x)

We showed that the two sides could take the same form

\Rightarrow True

tan (\frac{π}{3}) sin (\frac{2}{3} π) = 1 + sin (\frac{π}{6})

csc (2 x) = \frac{2 3}{3}

tan (x) = sin (x) - cos (x)

tan (\frac{11}{12} π) = tan (- \frac{π}{12})

cot (B) sec (B) sin (B) = 1

Is sin(5x)-sin(x)=2cos(3x)sin(2x) ?
The answer to whether sin(5x)-sin(x)=2cos(3x)sin(2x) is True