Question

Simplify (SecX-TanX)(1+sinX) X stands for theta

Answer 1

`\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\ -------------------------------`


`\bf [sec(\theta )-tan(\theta )][1+sin(\theta )]\implies \left[ (1)/(cos(\theta ))-(sin(\theta ))/(cos(\theta )) \right][1+sin(\theta )] \\\\\\\ \left[(1-sin(\theta ))/(cos(\theta )) \right][1+sin(\theta )]\implies \cfrac{\stackrel{\textit{difference of squares}}{[1-sin(\theta )][1+sin(\theta )]}}{cos(\theta )} \\\\\\ \cfrac{1^2-sin^2(\theta )}{cos(\theta )}\implies \cfrac{cos^2(\theta )}{cos(\theta )}\implies cos(\theta )`