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| 1. |
Sin 780°.Sin120°+Cos240°.Sin390°=1/2 |
| Answer» Ans.\xa0\\(Sin 780°.Sin120°+Cos240°.Sin390°={1\\over 2}\\)Taking LHS\\(Sin 780°.Sin120°+Cos240°.Sin390°\\)=>\xa0\\(Sin( 2\\times 360°+60°).Sin(180°-60°)+Cos(180°+60°).Sin(360°+30°)\\)\\(=> Sin( 4\\pi+60°).Sin(\\pi-60°)+Cos(\\pi+60°).Sin(2\\pi+30°)\\)=>\xa0\\(Sin60°.Sin60°- Cos60°.Sin30°\\)=>\xa0\\({\\sqrt 3\\over 2}.{\\sqrt 3\\over 2} - {1\\over 2}.{1\\over 2} = {3\\over 4} - {1\\over 4} \\)=>\xa0\\({2\\over 4 } = {1\\over 2 } = RHS \\)Hence Proved | |