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प्रश्न
sin 163° cos 347° + sin 73° sin 167° =
पर्याय
0
- \[\frac{1}{2}\]
1
None of these
उत्तर
\[\sin163^\circ\cos347^\circ + \sin73^\circ\sin167^\circ\]
\[ = \sin\left( 180^\circ - 17^\circ \right)\cos\left( 360^\circ - 13^\circ \right) + \sin\left( 90^\circ - 17^\circ \right)\sin\left( 180^\circ - 13^\circ \right)\]
\[ = \sin17^\circ\cos13^\circ + \cos17^\circ\sin13^\circ\]
\[ = \sin\left( 17^\circ + 13^\circ \right) \left[ \sin\left( A + B \right) = \sin A\cos B + \sin B\cos A \right]\]
\[ = \sin30^\circ\]
\[ = \frac{1}{2}\]
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