Question

prove that tan A/cot A = Sec²A/cosec²A​

Answer 1

Step-by-step explanation:

$\frac{ tana}{cota} = \frac{sec {}^{2}a }{cosec {}^{2}a } \\ l.h.s \\ \frac{tana}{cota} = \frac{ \frac{sina}{cosa} }{ \frac{cosa}{sina} } \\ = \frac{sina \times sina}{cosa \times cosa} \\ = \frac{sin {}^{2} a}{cos {}^{2}a } \\ \\ r.h.s \\ \frac{sec {}^{2}a }{cosec {}^{2}a } = \frac{ \frac{1}{cos {}^{2} a} }{ \frac{1}{sin {}^{2}a } } \\ = \frac{sin {}^{2} a}{cos {}^{2} a} \\ l.h.s. = r.h.s \\ hence \: proved \\ \\ \\ formulas \\ 1)tana = \frac{sina}{cosa} \\ 2)cota = \frac{cosa}{sina} \\ 3)seca = \frac{1}{cosa} \\ 4)coseca = \frac{1}{sina}$