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Prove that :sin 420^@ cos390^@+cos(-300^...

Prove that :`sin 420^@ cos390^@+cos(-300^@)sin(-330^@)=1`

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`L.H.S. = sin420^@cos390^@+cos(-300^@)sin(-330^@)`
`=sin(2pi+60)^@cos(2pi+30)^@+cos(300^@)(-sin330^@)`
`=sin(2pi+60)^@cos(2pi+30)^@-cos(2pi-60)^@(sin(2pi-30)^@)`
`=sin60^@cos30^@-cos60^@(-sin30^@)`
`=sin60^@cos30^@+cos60^@sin30^@`
We know, `sinAcosB +cosAsinB = sin(A+B).`
`:. sin60^@cos30^@+cos60^@sin30^@ = sin(60+30)^@`
`=sin90^@ = 1 = R.H.S.`
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