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  4. What is the value of sin 10° + sin 50° - sin 70° ?

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Q. What is the value of $\sin \, 10^{\circ} + \sin \, 50^{\circ} - \sin \, 70^{\circ}$ ?

Trigonometric Functions

Solution:

The given expression $\sin \, 10^{\circ} + \sin \, 50^{\circ} - \sin \, 70^{\circ}$ can also be written as $\sin \, 10^{\circ} - (\sin \, 70^{\circ} - \sin \, 50^{\circ})$
$= \sin \, 10^{\circ} - (2 \, \cos \, 60^{\circ} \, \sin \, 10^{\circ})$
$= \sin \, 10^{\circ} (2 \, \cos \, 60^{\circ} - 1) = \sin \, 10^{\circ}( 1 - 1) = 0$