(sin 90° - tan 60°)/(tan 60° - cos 0°)
= (1 - tan 60°)/(tan 60° - cos 0°)
= (1 - √3)/(tan 60° - cos 0°)
= (1 - √3)/(√3 - cos 0°)
= (1 - √3)/(√3 - 1)
= ((1 - √3)) × ((√3 + 1))/((√3 - 1)) × ((√3 + 1))
= ((1 - √3)) × ((√3 + 1))/((√3)² - 1
= ((1 - √3) × (√3 + 1))/(3 - 1)
= ((1 - √3) × (√3 + 1))/2
= (1 - (√3)²/2
= (1 - 3)/2
= -2/2
= -1
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Verified answer
(sin 90° - tan 60°)/(tan 60° - cos 0°)
= (1 - tan 60°)/(tan 60° - cos 0°)
= (1 - √3)/(tan 60° - cos 0°)
= (1 - √3)/(√3 - cos 0°)
= (1 - √3)/(√3 - 1)
= ((1 - √3)) × ((√3 + 1))/((√3 - 1)) × ((√3 + 1))
= ((1 - √3)) × ((√3 + 1))/((√3)² - 1
= ((1 - √3) × (√3 + 1))/(3 - 1)
= ((1 - √3) × (√3 + 1))/2
= (1 - (√3)²/2
= (1 - 3)/2
= -2/2
= -1