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Question Number 11285 by uni last updated on 19/Mar/17

$$\frac{sin20}{cos80-tan30\times sin80}=?$$

Answered by mrW1 last updated on 19/Mar/17

$$=\frac{sin20}{cos80-\frac{\sin 30}{\cos 30}\times sin80}$$$$=\frac{sin20\times \cos 30}{\cos 30\times cos80-\sin 30\times sin80}$$$$=\frac{sin20\times \cos 30}{\cos 110}$$$$=\frac{sin20\times \cos 30}{-\sin 20}$$$$=-\cos 30$$$$=-\frac{\sqrt{3}}{2}$$

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