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Sagot :
Let's prove
[tex]\boxed{\sf 1+tan^2\theta(1-sin^2\theta)=1}[/tex]
LHS
[tex]\\ \sf\longmapsto 1+tan^2\theta(1-sin^2\theta)[/tex]
[tex]\\ \sf\longmapsto 1+\dfrac{sin^2\theta}{cos^2\theta}(1-sin^2\theta)[/tex]
[tex]\\ \sf\longmapsto \dfrac{cos^2\theta+sin^2\theta}{cos^2\theta}(1-sin^2\theta)[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{cos^2\theta}(1-sin^2\theta)[/tex]
[tex]\\ \sf\longmapsto \dfrac{1-sin^2\theta}{cos^2\theta}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1-sin^2\theta}{1-sin^2\theta}[/tex]
[tex]\\ \sf\longmapsto 1[/tex]
Hence provee
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