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Question

Prove that cos 510cos 330+sin 390cos 120=1

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Solution

cos 510=cos(330+150)=cos150=cos(18030)=cos30
​​​​​​​cos 510=cos(54030)=cos 30
cos 330=cos(36030)=+cos 30
sin 390=sin(360+30)=sin30
cos 120=cos(90+30)=sin30
So the given expression changes to - cos230sin230
= (sin230+cos230)
= - 1

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