Solution
67)
[tex]\begin{gathered} sec\theta\text{ = }\frac{1}{cos\theta} \\ Cross\text{ multiply} \\ sec\theta\text{ }\times\text{ cos}\theta \\ \frac{1}{cos\theta}\text{ }\times cos\theta \\ =\text{ 1} \end{gathered}[/tex]
68)
Draw a right angle triangle:
[tex]\begin{gathered} sin\theta\text{ = }\frac{opposite}{hypotenuse}\text{ = }\frac{a}{c} \\ cos\theta\text{ = }\frac{adjacent\text{ }}{Hypotenuse}\text{ = }\frac{b}{c} \\ tan\theta\text{ = }\frac{opposite}{adjacent\text{ }}\text{ = }\frac{a}{b} \end{gathered}[/tex][tex]\begin{gathered} \\ \frac{sin\theta\begin{equation*}\end{equation*}}{cos\theta}\text{ = }\frac{a}{c}\text{ }\div\text{ }\frac{b}{c} \\ =\text{ }\frac{a}{c}\text{ }\times\text{ }\frac{c}{b} \\ =\text{ }\frac{a}{b} \\ Hence,tan\theta\text{= }\frac{sin\theta}{cos\theta} \end{gathered}[/tex]
