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Prove that: `sin(-420^(@))cos390^(@)+cos(-660^(@))sin330^(@)=1`

Answer» LHS `=sin(-420^(@))cos390^(@) + cos(-660^(@))sin330^(@)`
`-sin420^(@)cos390^(@)+cos660^(@)sin330^(@)`
`=-sin(360^(@)+60^(@))cos(360^(@)+30^(@))+cos(360^(@)+300^(@))sin(360^(@)+30^(@))`
`=-sin60^(@)cos30^(@)+cos300^(@)(-sin30^(@))`
`=-sqrt(3)/2 xx sqrt(3)/2-1/2cos(360^(@))-60^(@)`
`=-3/4-1/2 cos60^(@)`
`=-3/4 -1/2 xx 1/2`
`-3/4 -1/4 =-1`
=RHS Hence proved.


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