Question
If $\cos\theta=\frac{2}{3},$ find the value of $\frac{\sec\theta-1}{\sec\theta+1}.$
✓
Answer
$\cos\theta=\frac{2}{3}\Rightarrow\sec\theta=\frac{3}{2}$
$\therefore\frac{\sec\theta-1}{\sec\theta+1}=\frac{\frac{3}{2}-1}{\frac{3}{2}+1}$
$=\frac{\frac{1}{2}}{\frac{5}{2}}=\frac{1}{2}\times\frac{2}{5}=\frac{1}{5}$
$\therefore\frac{\sec\theta-1}{\sec\theta+1}=\frac{\frac{3}{2}-1}{\frac{3}{2}+1}$
$=\frac{\frac{1}{2}}{\frac{5}{2}}=\frac{1}{2}\times\frac{2}{5}=\frac{1}{5}$
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