Question

If $\cos A=\frac{7}{25}$, find the value of $\tan A+\cot A.$

Answer 1

$\cos A=\frac{7}{25}$

$\Rightarrow \sin A=\sqrt{1-{\cos }^{2}A}$

$=\sqrt{1-{\left(\frac{7}{25}\right)}^2}$

$=\sqrt{\frac{625-49}{625}}$

$=\sqrt{\frac{576}{625}}$

$\therefore \sin A=\frac{24}{25}$

$\tan A+\cot A=\frac{\sin A}{\cos A}+\frac{\cos A}{\sin A}$

$=\frac{\frac{24}{25}}{\frac{7}{25}}+\frac{\frac{7}{25}}{\frac{24}{25}}$

$=\frac{24}{7}+\frac{7}{24}$

$=\frac{576+49}{168}=\frac{745}{168}$