If cot A = 5/12, then sin A + cos A is ………A) 17/13B) 12/13C) 5/

1.	If cot A = 5/12, then sin A + cos A is ………A) 17/13B) 12/13C) 5/13D) 20/13
Answer» Correct option is: A) \(\frac{17}{13}\) We have cot A = \(\frac 5{12}\) \(\therefore\) \(1 + cot^2A = 1 + (\frac 5 {12})^2 = 1 + \frac {25}{144} \) = \(\frac {144+25}{144} = \frac {169}{144} = (\frac {13}{12})^2\) = \(cosec^2A = (\frac {13}{12})^2\) (\(\because\) \(1 + cot^2A = cosec^2A\)) = cosec A = \(\frac {13}{12}\) \(\therefore\) Sin A = \(\frac {1}{cosec \,A} = \frac 1{\frac {13}{12}} = \frac {12}{13}\) \(\therefore\) cot A = \(\frac {cos\, A}{sin \, A} = \frac 5{12}\) = cos A = \(\frac 5{12}\) sin A = \(\frac 5{12}\) \(\times\) \(\frac {12}{13}\) = \(\frac 5{13}\) \(\therefore\) Sin A + cos A = \(\frac {12}{13}\) + \(\frac 5{13}\) = \(\frac {17}{13}\) Correct option is: A) \(\frac{17}{13}\)

If cot A = 5/12, then sin A + cos A is ………A) 17/13B) 12/13C) 5/13D) 20/13

Answer»

Correct option is: A) \(\frac{17}{13}\)

We have cot A = \(\frac 5{12}\)

\(\therefore\) \(1 + cot^2A = 1 + (\frac 5 {12})^2 = 1 + \frac {25}{144} \)

= \(\frac {144+25}{144} = \frac {169}{144} = (\frac {13}{12})^2\)

= \(cosec^2A = (\frac {13}{12})^2\) (\(\because\) \(1 + cot^2A = cosec^2A\))

= cosec A = \(\frac {13}{12}\)

\(\therefore\) Sin A = \(\frac {1}{cosec \,A} = \frac 1{\frac {13}{12}} = \frac {12}{13}\)

\(\therefore\) cot A = \(\frac {cos\, A}{sin \, A} = \frac 5{12}\)

= cos A = \(\frac 5{12}\) sin A = \(\frac 5{12}\) \(\times\) \(\frac {12}{13}\) = \(\frac 5{13}\)

\(\therefore\) Sin A + cos A = \(\frac {12}{13}\) + \(\frac 5{13}\) = \(\frac {17}{13}\)

Correct option is: A) \(\frac{17}{13}\)