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Question Number 199830 by cortano12 last updated on 10/Nov/23

$$\mathrm{Si}\cos \mathrm{x}+\sin \mathrm{x}=\frac{1+\sqrt{3}}{2},$$$$\mathrm{halle}\mathrm{el}\mathrm{valor}\mathrm{de}\mathrm{la}\mathrm{expresion}$$$$\mathrm{R}=16(\sin {}^6\mathrm{x}+\cos {}^6\mathrm{x})+3(\sec {}^2\mathrm{x}+{\csc }^2\mathrm{x})$$

Answered by Frix last updated on 10/Nov/23

$$\cos x+\sin x=c\Rightarrow$$$$x={2\tan }^{-1}\frac{1\pm \sqrt{2-c^2}}{c+1}[+2n\pi ]$$$$c=\frac{1+\sqrt{3}}{2}\Rightarrow x=\frac{\pi }{6}\vee x=\frac{\pi }{3}$$$$R=23$$

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