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Radical Trigonometry

If

\[\sin(x+y) = 2\sin\big(\tfrac{1}{2}(x-y)\big) \]

\[ \sin(y+z) = 2\sin\big(\tfrac{1}{2}(y-z)\big) \]

Prove That

\[ \big(\tfrac{1}{2}\sin x\cos z\big)^{1/4}+\big(\tfrac{1}{2}\cos x\sin z\big)^{1/4} =\big(\sin 2y)^{1/12}\]

Note : \(x\), \(y\) and \(z\) are acute angles.


This is a part of the set Formidable Series and Integrals

Note by Ishan Singh
9 months, 2 weeks ago

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