Solve the equation over the interval 0 degree 360 degree 20s

Solve the equation over the interval [0 degree, 360 degree] 20sec^2 theta - 3sec theta - 35 = 0 (Round to the nearest tenth. List values from smallest to

Solution

i am taking theta as \'x\'

20sec^2(x) -3secx -35=0

20sec^2(x) -28secx+25secx-35=0

4secx(5secx -7) +5(5secx-7)=0

(4secx+5) (5secx -7)=0

so secx = -5/4 or secx =7/5

so x = 143.1,216.9 degree , 44.4 degree,315 degree