Solving sin⁡2xsin⁡x+cos2x=sin⁡5xsin⁡4x+cos24x

Rudy Koch

Rudy Koch

Answered

2022-01-23

Solving sin2xsinx+cos2x=sin5xsin4x+cos24x

Answer & Explanation

oferenteoo

oferenteoo

Expert

2022-01-24Added 12 answers

Use cos2(a)+sin2(a)=1 first on both sides then factorize.
sin(x)[sin(2x)sin(x)]=sin(4x)[sin(5x)sin(4x)]
Now use sin(A)sin(B) as a product on both sides and simplify (giving some roots sin(x2)=0)
sin(x)2cos(3x2)sin(x2)=sin(4x)2cos(9x2)sin(x2)
then write sin(C)cos(D) as a difference of sines on both sides and simplify.
12sin(5x2)+sin(x2)=12sin(17x2)+sin(x2)
Write the difference of sines as a product and solve
sin(5x2)sin(17x2)=0

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