Sin 780°.Sin120°+Cos240°.Sin390°=1/2
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Posted by Roma Lohia 7 years, 1 month ago
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Naveen Sharma 7 years, 1 month ago
Ans. \(Sin 780°.Sin120°+Cos240°.Sin390°={1\over 2}\)
Taking LHS
\(Sin 780°.Sin120°+Cos240°.Sin390°\)
=> \(Sin( 2\times 360°+60°).Sin(180°-60°)+Cos(180°+60°).Sin(360°+30°)\)
\(=> Sin( 4\pi+60°).Sin(\pi-60°)+Cos(\pi+60°).Sin(2\pi+30°)\)
=> \(Sin60°.Sin60°- Cos60°.Sin30°\)
=> \({\sqrt 3\over 2}.{\sqrt 3\over 2} - {1\over 2}.{1\over 2} = {3\over 4} - {1\over 4} \)
=> \({2\over 4 } = {1\over 2 } = RHS \)
Hence Proved
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