Question

Given $\cos \theta =\frac{21}{29}$, what the value of $\frac{\sec \theta }{\tan \theta -\sin \theta }$?

Answer 1

$\cos \theta =\frac{OM}{OP}=\frac{21}{29}$
$PM=\sqrt{{29}^2-{21}^2}=\sqrt{841-441}$
$=\sqrt{400}=20$
$\therefore \frac{\sec \theta }{\tan \theta -\sin \theta }=\frac{\frac{21}{29}}{\frac{20}{21}-\frac{20}{29}}$
$=\frac{29\times 29}{580-420}=\frac{841}{160}=5\frac{41}{160}$