![\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta )=1-sin^2(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{[cos(x)]^2[tan(x)]^2-1}{[cos(x)]^2}\implies \cfrac{cos^2(x)tan^2(x)-1}{cos^2(x)}\implies \cfrac{cos^2(x)\frac{sin^2(x)}{cos^2(x)}-1}{cos^2(x)} \\\\\\ \cfrac{sin^2(x)-1}{cos^2(x)}\implies \cfrac{-[1-sin^2(x)]}{cos^2(x)}\implies \cfrac{-cos^2(x)}{cos^2(x)}\implies -1](/tpl/images/0396/7811/b7117.png)
(cos x)^2 (tan x)^2 -1 …divided by… (cos x)^2
simplify.
...
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