Question : In a right-angled $\triangle PQR$, PQ = 5 cm, QR = 13 cm and $\angle P=90^{\circ}$. Find the value of $\tan Q-\tan R$.
Option 1: $\frac{5}{14}$
Option 2: $\frac{119}{60}$
Option 3: $\frac{60}{119}$
Option 4: $\frac{14}{5}$
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Correct Answer: $\frac{119}{60}$
Solution : Given: PQ = 5 cm QR = 13 cm $\angle P=90^{\circ}$ In $\triangle PQR$, $RQ^2=PQ^2+PR^2$ ⇒ $13^2=5^2+PR^2$ ⇒ $PR^2=169-25$ ⇒ $PR^2=144$ $\therefore PR = 12$ Now, $\tan Q-\tan R$ $=\frac{12}{5}-\frac{5}{12}$ $=\frac{144-25}{60}$ $=\frac{119}{60}$ Hence, the correct answer is $\frac{119}{60}$.
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