Question

solve showing all steps, sec^2x-2.5=0 on the interval of [0,2pi] in degrees

Answer 1

secx -2.5 = 0 Given, Ittan? 2 20 5 (: sec²a = 1+tanto) Inirs tana 1.5 tana Itana + 1.225 a 2 we know, if tana = tana then n(180°) + x Case 1 :- when tana 1.225 tana = tan (50.77°) we have da 50.77° Put this value of x in ③ x= n(180°) + 50.77°

Put n0 X= 50.77° Put n=1, de = 180+ 50.77° 230.770 Thus X = 50.77°, 230.770 Case (1) - when taus when taux = -1.225 tant = ban (-50-77') we have a = - 50.77° Put this value of a in ① x= n(180°) - 50.77° Put nal, x=180°– 50.77° = 129-23° Put = 2(180°) -50.77° - 309.23 Thus solution of the given equation is n=2, 20 0 X = 50.77°, 129.239, 230.77°, 309.23°