Question : $\triangle PQR$ is right angled at Q. If PQ = 12 cm and PR = 13 cm, find $\tan P+\cot R$.
Option 1: $\frac{9}{10}$
Option 2: $0$
Option 3: $\frac{10}{12}$
Option 4: $\frac{12}{10}$
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Correct Answer: $\frac{10}{12}$
Solution : PQ = 12 cm PR = 13 cm By Pythagoras theorem, PR 2 = PQ 2 + QR 2 13 2 = 12 2 + QR 2 QR 2 = 169 – 144 = 25 ⇒ QR = 5 cm $\tan P$ = $\frac{5}{12}$ ⇒ $\cot R$ = $\frac{5}{12}$ ⇒ $\tan P+\cot R$ = $\frac{5}{12}$+$\frac{5}{12}$ = $\frac{10}{12}$ Hence, the correct answer is $\frac{10}{12}$.
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