Question

If 2sin²Φ+ 2cosΦ+ 1/4=0 then the general equation is?

Answer 1

2( 1- cos²∅) + 2cos∅ + 1/4 = 0

2 - 2cos²∅ +2cos∅ + 1/4 = 0

-2cos²∅ +2cos∅ + 9/4 = 0

-8cos²∅ + 8cos∅ + 9 = 0

8cos²∅ - 8cos∅ - 9 = 0

cos∅ = { 8 ± √352}/16

18 < √352 < 19

let √352 ≈ 18.7 ( approx )
then,

cos∅ = ( 8 -18.7)/16 , (8+18.7)/16

cos∅ ≠ ( 8 + 18.7)/16 becoz max value of cos = 1

so,
cos ∅ = ( -10.7)/16

∅ = 2nπ ± cos^-1( -10.7)/16