Prove that: `sin(-420^0)(cos390^0)+cos(-660^0)(sin330^0)=-1.`

Explanation

Here, we will use ,

`sin(-theta) = - sin theta and cos(-theta) =cos theta`

Now,

`L.H.S. = sin(-420^@)cos390^@+cos(-660^@)sin330^@`

`=-sin(420^@)cos390^@+cos(660^@)sin330^@`

`=-sin(360^@+60^@)cos(360^@+30^@)+cos(2*360^@ - 60^@)sin(360^@-30^@)`

`=-sin(60^@)cos(30^@)+cos(60^@)(-sin(30^@))`

`=-(sqrt3/2)(sqrt3/2)+(1/2)(-1/2)`

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