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Prove that: sin600^0cos 390^0+cos 480^0s...

Prove that: `sin600^0cos 390^0+cos 480^0sin 150^0=-1`

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`LHS=sin600cos390 + cos 480sin150`

`=sin(6x90+60).cos(4x90+30) + cos(5x90+30)sin(90+60) `

`=(-sin60).cos30 +-sin30.cos60`

`= -√3/2 x √3/2 +(-1/2 x 1/2)`

`= -3/4-1/4`

`=-1=RHS`

Hence, proved.
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Knowledge Check

  • The value of sin 600^(@) cos 330^(@)+ cos 120^(@) sin 150^(@) is

    A
    `-1`
    B
    1
    C
    `(1)/(sqrt2)`
    D
    `(sqrt3)/(2)`

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