Verified by Ajay Kumar
If \(\cos A=\frac{12}{13}\), find the values of \(\sin A\) and \(\cot A\).
\(\frac{5}{13}\) and \(\frac{7}{12}\)
\(\frac{7}{8}\) and \(\frac{8}{9}\)
\(\frac{5}{13}\) and \(\frac{12}{5}\)
\(\frac{5}{6}\) and \(\frac{6}{7}\)
Answer: C
Given \(\cos A=\frac{12}{13}\). Using \(\sin^2A+\cos^2A=1\), \(\sin^2A=1-\left(\frac{12}{13}\right)^2=\frac{25}{169}\). Therefore, \(\sin A=\frac{5}{13}\). Now, \(\cot A=\frac{\cos A}{\sin A}=\frac{12/13}{5/13}=\frac{12}{5}\). Trick: Recognise the 5-12-13 right triangle.
अगर \(\cos A=\frac{12}{13}\), \(\sin A\) और \(\cot A\) के मान ज्ञात कीजिए।
\(\frac{5}{13}\) और \(\frac{7}{12}\)
\(\frac{7}{8}\) और \(\frac{8}{9}\)
\(\frac{5}{13}\) और \(\frac{12}{5}\)
\(\frac{5}{6}\) और \(\frac{6}{7}\)
उत्तर: C
दिया गया है \(\cos A=\frac{12}{13}\)। सूत्र \(\sin^2A+\cos^2A=1\) से, \(\sin^2A=1-\left(\frac{12}{13}\right)^2=\frac{25}{169}\)। अतः \(\sin A=\frac{5}{13}\)। अब, \(\cot A=\frac{\cos A}{\sin A}=\frac{12/13}{5/13}=\frac{12}{5}\)। ट्रिक: 5-12-13 समकोण त्रिभुज को पहचानें।
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