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Georgiiaa · Apr 5, 2020

Can someone please help me with this?

thanks!!

Drdusk · Apr 5, 2020

Georgiiaa said:
Can someone please help me with this?

thanks!!

$\text{I would just start with the RHS and expand it using the formulas on the formula sheet}$

$\sin(a + b) = \sin a \cos b + \cos a \sin b$

$\sin(a - b) = \sin a \cos b - \cos a \sin b$

$\text{The result follows trivially}$

CM_Tutor · Apr 5, 2020

Drdusk said:
$\text{I would just start with the RHS and expand it using the formulas on the formula sheet}$

$\sin(a + b) = \sin a \cos b + \cos a \sin b$

$\sin(a - b) = \sin a \cos b - \cos a \sin b$

$\text{The result follows trivially}$

It can also follow from the two results quoted by Drdusk, by adding them to get

$\sin(a + b) + \sin(a - b) = 2 \sin a \cos b$

and then let $a = 7x$ and $b = 3x$ , from which the result follows:

$\sin(7x + 3x) + \sin(7x - 3x) = 2 \sin 7x \cos 3x$

or more typically

$\cfrac{1}{2}(\sin 10x + \sin 4x) = \sin 7x \cos 3x$

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