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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
7 months, 2 weeks ago