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Question Number 148767 by mim24 last updated on 31/Jul/21

Answered by liberty last updated on 31/Jul/21

$$\frac{1}{\sin 20°}+\frac{\sqrt{3}}{\cos 20°}=\frac{\cos 20°+\sqrt{3}\sin 20°}{\sin 20°\cos 20°}$$$$=\frac{\frac{1}{2}\cos 20°+\frac{\sqrt{3}\sin 20°}{2}}{\frac{1}{4}\sin 40°}$$$$=\frac{\sin 30°\cos 20°+\cos 30°\sin 20°}{\frac{1}{4}\sin 40°}$$$$=\frac{4\sin 50°}{\cos 50°}=4\tan 50°=4\cot 40°$$

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