Mathematics: Rewrite with only sin x and cos x. sin 3x

Rewrite with only sin x and cos x. sin 3x - id31472233, brainlord2848

Ответ:

fhemmie963

15.03.2022

$\bf sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}})
\\\\\\
sin(2\theta)=2sin(\theta)cos(\theta)
\\ \quad \\
cos(2\theta)=
\begin{cases}
\boxed{cos^2(\theta)-sin^2(\theta)}\\
1-2sin^2(\theta)\\
2cos^2(\theta)-1
\end{cases}\\\\
-------------------------------\\\\
sin(3x)\implies sin(2x+x)\implies sin(2x)cos(x)+cos(2x)sin(x)$

$\bf 2sin(x)cos(x)cos(x)~+~[cos^2(x)-sin^2(x)]sin(x)
\\\\\\
\stackrel{like~terms}{\stackrel{\downarrow }{2sin(x)cos^2(x)}~~+~~\stackrel{\downarrow }{sin(x)cos^2(x)}}-sin^3(x)
\\\\\\
3sin(x)cos^2(x)-sin^3(x)$

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Rewrite with only sin x and cos x. sin 3x

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