Question : If $\cos A=\frac{63}{65}$, then find the value of $\tan A+\cot A$ (up to two places of decimal).
Option 1: 4.19
Option 2: 2.76
Option 3: 3.19
Option 4: 5.23
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Correct Answer: 4.19
Solution :
Given, $\cos A=\frac{63}{65}$
We know, $\sin A = \sqrt{1-\cos^2 A}$
$⇒\sin A = \sqrt{1-(\frac{63}{65})^2}$
$⇒\sin A = \sqrt{(\frac{256}{65^2})}$
$\therefore \sin A =\frac{16}{65}$
Now, $\tan A+\cot A$
= $\frac{\sin A}{\cos A}+\frac{\cos A}{\sin A}$
= $\frac{\sin^2 A + \cos^2 A}{\sin A \cos A}$
= $\frac{1}{\sin A \cos A}$
= $\frac{65\times 65}{63\times 16}$
= $4.19$
Hence, the correct answer is 4.19.
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