Question

Simplify secx-sinxtanx

Answer 1

`\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\qquad \qquad sec(\theta)=\cfrac{1}{cos(\theta)} \\\\\\ \textit{also recall }sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\ -------------------------------\\\\ sec(x)-sin(x)tan(x)\implies \cfrac{1}{cos(x)}-sin(x)\cdot \cfrac{sin(x)}{cos(x)} \\\\\\\cfrac{1}{cos(x)}-\cfrac{sin^2(x)}{cos(x)}\implies \cfrac{1-sin^2(x)}{cos(x)}\implies \cfrac{cos^2(x)}{cos(x)}\implies cos(x)`