Question

sin 163° cos 347° + sin 73° sin 167° =

Options

• 0

• \[\frac{1}{2}\]

   

• 1

• None of these

Answer 1

\[\frac{1}{2}\]

\[\sin163^\circ\cos347^\circ + \sin73^\circ\sin167^\circ\]
\[ = \sin\left( 180^\circ - 17^\circ \right)\cos\left( 360^\circ - 13^\circ \right) + \sin\left( 90^\circ - 17^\circ \right)\sin\left( 180^\circ - 13^\circ \right)\]
\[ = \sin17^\circ\cos13^\circ + \cos17^\circ\sin13^\circ\]
\[ = \sin\left( 17^\circ + 13^\circ \right) \left[ \sin\left( A + B \right) = \sin A\cos B + \sin B\cos A \right]\]
\[ = \sin30^\circ\]
\[ = \frac{1}{2}\]