Question

if sec-tan=4 then prove that cos=8/17

Answer 1

Sec - tan = 4 -----(1)
now multiplying the first term with sec+tan and devided with sec+tan....
or, sec-tan x (sec+tan / sec+tan) = 4

or, (sec-tan) (sec+tan) / sec+tan = 4

or, sec²-tan² / sec+tan = 4

or, 1/sec+tan = 4

or, sec+tan = 1/4 -----(2)


so, now (1)+(2)
sec - tan = 4
sec + tan = 1/4
or, 2sec = 4+1/4
or, 2sec = 17/4
or, sec = 17/8
or, cos = 1/sec
or, cos = 8/17------(provedp