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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