Question

prove=sin600 cos 390 + cos480 sin150=-1

Answer 1

sin600° = sin(2×360°-120°)
= -sin120°=-√3/2

cos390° =cos(360°+30°)
=cos30° = √3/2

cos480°= cos(360°+120°)
= cos120° = -1/2

sin150° = sin(180°-30°) =1/2

put this value in LHS

LHS = -√3/2 × √3/2 + (-1/2 )× 1/2
= -3/4 -1/4
= -4/4 = -1 = RHS

Answer 2

L.H.S

= sin600°cos390° + cos480°sin150°

= sin240° cos30° + cos120°sin150°

= sin(270-30) cos30 + cos(90+30) sin(180-30)

= (-cos30°.cos30°) + (-sin30°.sin30°)

= -1 [sin²30°+cos²30°]

= -1×1

= -1

= R.H.S
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