Question

sin 780 sin 480 + cos 120 sin 150 = 1/2

Answer 1

Here u go

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Answer 2

Step-by-step explanation:

We know that

$sin(2n\pi + \theta) = sin \: \theta \\ cos(90 + \theta) = - sin \: \theta$

$= > sin 780° \: sin 480° + cos 120° \: sin 150° \\ \\ = > sin(4\pi + 60°) \: sin(2\pi + 120°) + cos(90° + 30°)sin(180° - 30°) \\ \\ = > sin \: 60° \: sin \: 120° + ( - sin \: 30°)( sin \: 30°) \\ \\ = > \frac{ \sqrt{3} }{2} \: sin \: (90° + 30°) + ( - \frac{1}{2} )( \frac{1}{2} ) \\ \\ = > \frac{ \sqrt{3} }{2} \: cos\: (30°) - \frac{1}{4} \\ \\ = > \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{3} }{2} - \frac{1}{4} \\ \\ = > \frac{3}{4} - \frac{1}{4} \\ \\ = > \frac{2}{4} \\ \\sin 780° \: sin 480° + cos 120° \: sin 150° = \frac{1}{2}$

Hence proved.

Hope it helps you.