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