Question

Which expression is equivalent to sin(1.8x) sin(0.5x)?

0.5[sin(2.3x) + sin(1.3x)]

0.5[sin(2.3x) − sin(1.3x)]

0.5[cos(1.3x) − cos(2.3x)]

0.5[cos(2.3x) − cos(1.3x)]

Answer 1

Hum, this problem was difficult.
You use the next expression to solve this problem.

\[\cos (A - B) = \cos A \cos B + \sin A \sin B \]
\[\cos (A + B) = \cos A \cos B - \sin A \sin B\]
\[\cos (A - B ) - \cos (A +B ) =2 \sin A \sin B\]

So
\[\sin A \sin B = 0.5 \left( \cos(A - B) - \cos(A + B) \right)\]

A = 1.8 x, B = 0.5 x
\[\sin (1.8x) \sin (0.5x) = 0.5\left( \cos(1.8-0.5)x - \cos(1.8+0.5)x \right)\]\[= 0.5 \left( \cos(1.3x) - \cos (2.3x) \right)\]

It's finish !!

Answer 2

thanks man for explaining it!!

Answer 3

Oh, don’t worry about it.