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Question Number 166686 by cortano1 last updated on 25/Feb/22

Commented by greogoury55 last updated on 26/Feb/22

$$\frac{1}{1-{\sin }^{2}10°}+\frac{2}{1-\cos 40°}+\frac{2}{1-\cos 80°}-2$$$$=\frac{1}{1-\cos {}^{2}80°}+\frac{2}{1-\cos 80°}+\frac{2}{1-\cos 40°}-2$$$$=\frac{1+2(1+\cos 80°)}{1-\cos {}^{2}80}+\frac{2}{1-\cos 40°}-2$$$$=\frac{3+2\cos 80°}{1-{\left(\frac{1+\cos 20°}{2}\right)}^2}+\frac{2}{1-\cos 40°}-2$$$$=\frac{12+8\cos 80°}{3-2\cos 20°-\cos {}^{2}20°}+\frac{2}{1-\cos 40°}-2$$$$$$

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