$\sin 480 ° \cos 690 ° + \cos 780 ° \sin 1050 ° =$

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$\frac{1}{2}$

answer is C.

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Detailed Solution

$\sin 480 ° \cos 690 ° + \cos 780 ° \sin 1050 °$

$= \sin (360 ° + 120 °) \cos (360 ° + 330 °) + \cos (360 ° + 420 °) \sin (3 \times 360 ° - 30 °)$

$= \sin 120 ° \cos 330 ° + \cos 420 ° (- \sin 30 °)$

$= \sin (90 ° + 30 °) \cos (360 ° - 30 °) + \cos (360 ° + 60 °) (- \sin 30 °)$

$= \cos 30 ° \times \cos 30 ° - \cos 60 ° \sin 30 °$

$= {(\frac{\sqrt{3}}{2})}^{2} - \frac{1}{2} \times \frac{1}{2} = \frac{3}{4} - \frac{1}{4} = \frac{1}{2}$

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