Question

If tanA = 3/4.find the value of cosec A and sec A​

Answer 1

Step-by-step explanation:

$\because \: {sec}^{2} A = 1 + {tan}^{2} A \\ \therefore \: {sec}^{2} A = 1 + ( \frac{3}{4} )^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1 + \frac{9}{16} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{16 + 9}{16} \\ \therefore \: {sec}^{2} A = \frac{25}{16} \\ \huge \purple {\boxed{\therefore \: {sec} A = \frac{5}{4}}} \\ \implies \: {cos} A = \frac{4}{5} \\ {sin } A ={cos} A\times {tan} A\\\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:=\frac{4}{5}\times \frac{3}{4}</p><p>\\\therefore {sin } A =\frac{3}{5}\\</p><p>\huge \purple {\boxed{ \therefore \: {cosec} A = \frac{5}{3}} }$