sin x+sin 3x=0

Reeves 2021-09-11 Answered
\(\displaystyle{\sin{{x}}}+{\sin{{3}}}{x}={0}\)

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Expert Answer

curwyrm
Answered 2021-09-12 Author has 16226 answers

\(\displaystyle{\sin{{x}}}+{\sin{{3}}}{x}={2}\frac{{\sin{{\left({3}{x}+{x}\right)}}}}{{2}}\times\frac{{\cos{{\left({3}{x}-{x}\right)}}}}{{2}}={0}\)
\(\displaystyle{2}{\sin{{2}}}{x}{\cos{{x}}}={0}\)
\(\displaystyle{\sin{{2}}}{x}={0}\) or \(\cos x=0\)
if \(\displaystyle{\sin{{2}}}{x}={0}\), then
\(\displaystyle{2}{x}={0}{\quad\text{or}\quad}\pi{\quad\text{or}\quad}{2}\pi\)
\(\displaystyle{x}={0},\frac{\pi}{{2}},\pi\)
if \(\displaystyle{\cos{{x}}}={0}\) then
\(\displaystyle{x}=\frac{\pi}{{2}},{3}\frac{\pi}{{2}}\)

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content_user
Answered 2021-10-12 Author has 2505 answers

Right answer is given below

 

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