Find the value of $sin 47^{\circ} + sin 61^{\circ} - sin 11^{\circ} - sin 25^{\circ}$

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Solution

Value of $sin 47^{\circ} + sin 61^{\circ} - sin 11^{\circ} - sin 25^{\circ} = (sin 47^{\circ} + sin 61^{\circ}) - (sin 11^{\circ} + sin 25^{\circ}) = 2 sin 54^{\circ} cos 7^{\circ} - 2 sin 18^{\circ} cos 7^{\circ} = 2 cos 7^{\circ} (sin 54^{\circ} - sin 18^{\circ})$
$= 2 cos 7^{\circ} (\frac{\sqrt{5} + 1}{4} - \frac{\sqrt{5} - 1}{4}) = cos 7^{\circ}$

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Similar questions

sin 47 ° + sin 61 ° - sin 11 ° - sin 25 °

x \in (0, 90^{\circ})

c o s x = s i n 61^{\circ} + s i n 47^{\circ} - s i n 25^{\circ} - s i n 11^{\circ}

sin 18^{\circ} = \frac{\sqrt{5} - 1}{4}

$cos 36^{\circ} = \frac{\sqrt{5} + 1}{4}$

\frac{(cos 11^{\circ} + sin 11^{\circ})}{(cos 11^{\circ} - sin 11^{\circ})}

\frac{(cos 11^{\circ} + sin 11^{\circ})}{(cos 11^{\circ} - sin 11^{\circ})}

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