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Question Number 140196 by mathdanisur last updated on 05/May/21

$$Calculate:\sqrt{3}cosec20°-sec20°$$

Answered by liberty last updated on 05/May/21

$$\frac{\sqrt{3}}{\sin 20°}-\frac{1}{\cos 20°}=$$$$\frac{2(\sqrt{3}\cos 20°-\sin 20°)}{\sin 40°}=$$$$\frac{4(\frac{\sqrt{3}}{2}\cos 20°-\frac{1}{2}\sin 20°)}{\sin 40°}=$$$$\frac{4(\cos 30°\cos 20°-\sin 30°\sin 20°)}{\sin 40°}=$$$$\frac{4\cos 50°}{\sin 40°}=4$$

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