Question

8sin75degree*sin45degree*sin105degree=root6+2root2

Answer 1

$8 \sin75° . \sin45°. \sin105° = \sqrt{6} + 2 \sqrt{2} \\ 8 \times \sin75° \times \frac{1}{ \sqrt{2} } \times \sin75° = \sqrt{6} + 2 \sqrt{2} \\ \frac{8}{ \sqrt{2} } \times ( \frac{ \sqrt{3} + 1}{2 \sqrt{2} } ) {}^{2} = \sqrt{6} + 2 \sqrt{2} \\ \frac{8}{ \sqrt{2} } \times ( \frac{ 4 + 2 \sqrt{3} }{8 } ) = \sqrt{6} + 2 \sqrt{2} \\ \frac{2 \sqrt{3} }{ \sqrt{2} } + \frac{4}{ \sqrt{2} } = \sqrt{6} + 2 \sqrt{2} \\ \sqrt{6} + 2 \sqrt{2} = \sqrt{6} + 2 \sqrt{2} \\LHS = RHS$

HENCE PROVED

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