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## Sagot :

[tex]=1+\frac{2sin^2\theta+2cos^2\theta}{sin\theta\ cos\theta}+\frac{sin^2\theta+cos^2\theta}{sin^2\theta\ cos^2\theta}\\\\=1+\frac{2(sin^2\theta+cos^2\theta)}{sin\theta\ cos\theta}+\frac{1}{sin^2\theta\ cos^2\theta}\\\\=1+\frac{2}{sin\theta\ cos\theta}+\frac{1}{sin^2\theta\ cos^2\theta}\\\\=1^2+2sec\theta\ cosec\theta+sec^2\theta\ cosec^2\theta\\\\=(1+sec\theta\ cosec\theta)^2=R[/tex]