![\bf sin(x)cos(x)[tan(x)+cot(x)]=1\\\\ -----------------------------\\\\ tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)} \qquad \qquad cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}\\\\ -----------------------------\\\\ thus \\\\\\ sin(x)cos(x)\left[ \cfrac{sin(x)}{cos(x)}+ \cfrac{cos(x)}{sin(x)}\right]\\\\\\ \boxed{sin(x)cos(x)}\left[ \cfrac{sin^2(x)+cos^2(x)}{\boxed{cos(x)sin(x)}}\right] \\\\\\ sin^2(x)+cos^2(x)\\\\ -----------------------------\\\\ recall\implies sin^2(\theta)+cos^2(\theta)=1](/tpl/images/0499/1880/08216.png)
Need on pre ! directions: verify each identity
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