Mathematics: Find a and b if sin2xcos3x = a sin 5x + b sin x

Find a and b if sin2xcos3x = a sin 5x + b sin

Ответ:

40029595

05.01.2022

Recall that

$\sin(x+y)=\sin x\cos y+\cos x\sin y$
$\sin(x-y)=\sin x\cos y-\cos x\sin y$

Adding these together, you have

$\sin(x+y)+\sin(x-y)=2\sin x\cos y$
$\dfrac12\sin(x+y)+\dfrac12\sin(x-y)=\sin x\cos y$

Replace

with

and

with

. You end up with

$\dfrac12\sin(2x+3x)+\dfrac12\sin(2x-3x)=\sin2x\cos3x$
$\sin2x\cos3x=\dfrac12\sin5x+\dfrac12\sin(-x)=\dfrac12\sin5x-\dfrac12\sin x$

and so $A=\dfrac12$ and $B=-\dfrac12$ .

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Ответ:

chartrow7

09.02.2022

Mathematics

24 square units

Step-by-step explanation:

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Find a and b if sin2xcos3x = a sin 5x + b sin x

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