[tex]\bf sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)
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tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\qquad \qquad sec(\theta)=\cfrac{1}{cos(\theta)}\\\\
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\cfrac{sec(x)-cos(x)}{sin(x)}\implies \cfrac{\frac{1}{cos(x)}-cos(x)}{sin(x)}\implies \cfrac{\frac{1-cos^2(x)}{cos(x)}}{sin(x)}\implies \cfrac{\frac{sin^2(x)}{cos(x)}}{\frac{sin(x)}{1}}
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[/tex]
[tex]\bf \cfrac{\underline{sin^2(x)}}{cos(x)}\cdot \cfrac{1}{\underline{sin(x)}}\implies \cfrac{sin(x)}{cos(x)}\implies tan(x)[/tex]
