Question

If cosecA=13/12 then find the value of tanA +cotA

Answer 1

Answer:

${cot}^{2} A \: = {cosec}^{2} A \: - 1 \\ = ( { \frac{13}{12} })^{2} - 1 \\ = \frac{169}{144} - 1 \\ = \frac{169 - 144}{144} = \frac{25}{144} \\ cot \: A \: = \frac{5}{12} \\ therefore \\ tan \: A = \frac{12}{5} \\ tan \: A + cot \: A = \frac{12}{5} + \frac{5}{12} \\ = \frac{12 \times 12 + 5 \times 5}{12 \times 5} \\ = \frac{144 + 25}{60} \\ = \frac{169}{60} \\ hence \\ tan \: A + cot \: A = \frac{169}{60} \\ \:$