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Question
Prove that: cos 510° cos 330° + sin 390° cos 120° = -1.
Solution
LHS = cos 510° cos 330° + sin 390° cos 120°
= cos(360° + 150°) cos(360° – 30°) + sin(360° + 30°) × cos(180° – 60°)
= cos 150° cos 30° + sin 30° (-cos 60°)
= cos(180° – 30°) cos 30° + sin 30° cos 60°
= -cos 30° cos 30° + `1/2 xx ((-1)/2)`
`= - sqrt3/2 xx sqrt3/2 - 1/2 xx 1/2`
`= - 3/4 - 1/4`
`= (- 3 - 1)/4`
= - 1
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