Question

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

Answer 1

$\cos A=\frac{7}{25}\therefore BC=\sqrt{{25}^2-7^2}=\sqrt{(25+7)(25-7)}=\sqrt{32\times 18}=\sqrt{4\times 4\times 2\times 2\times 9}=4\times 2\times 3=24\therefore BC=24\therefore \tan A+\cot A=\frac{24}{7}+\frac{7}{24}=\frac{{24}^2+7^2}{24\times 7}=\frac{625}{168}$