Question

Prove that sin420 cos390 + cos(-300 )sin(-330)= 1

Answer 1

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Answer 2

Sin 420 = sin (360+60) = sin 60 = √3/2
cos 390 = cos (360+30) = cos 30 = √3/2

cos (-300) = cos 300 = cos(360 - 60) = cos 60 = 1/2
sin (-330) = sin (360 + (-330) ) = sin 30 = 1/2

LHS = √3/2 * √3/2  + 1/2 * 1/2 = 1