Prove that: 7^ 14^ 28^ 56^ = 68^ 16 83^ - Vidyadip

Question

Prove that:
$\cos7^\circ\cos14^\circ\cos28^\circ\cos56^\circ=\frac{\sin68^\circ}{16\cos83^\circ}$

✓

Answer

$\text{LHS}=\cos7^\circ\cos14^\circ\cos28^\circ\cos56^\circ$
Divide and miltiply by $2\sin7^\circ,$ weget
$\frac{1}{2\sin7^\circ}.2\sin7^\circ.\cos14^\circ.\cos28^\circ.\cos56^\circ$
$=\frac{2\sin14^\circ}{2.2\sin7^\circ}.2\cos14^\circ.\cos28^\circ.\cos56^\circ$
$=\frac{2\sin28^\circ}{2.4\sin7^\circ}.\cos28^\circ.\cos56^\circ$
$=\frac{2\sin56^\circ}{2.8\sin7^\circ}.\cos56^\circ$
$=\frac{\sin112^\circ}{16\sin7^\circ}$
$=\frac{\sin(180^\circ-68^\circ)}{16\sin(90^\circ-83^\circ)}$
$=\frac{\sin68^\circ}{16\cos83^\circ}=\text{RHS}$

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