Question

If costheta+sectheta=5/2 the general value of theta is

Answer 1

Step-by-step explanation:

I'm replacing theta with "x" for my convinence

cosx+secx=5/2

cosx+1/cosx=5/2

[(cosx) ^2+1]/cosx=5/2

2[(cosx)^2+1]=5cosx

2cos^2 x-5cosx+1=0

solving this quadratic equation we get

cosx=-1/2 (or) cosx=-9/2

cosx=-cos2π/3 it doesn't exist

cosx=cos(π-2π/3) because cosx

cosx=cos2π/3 range is [-1, 1]

X=2nπ±2π/3

The general solution of X is 2nπ±2π/3