9cos4w30cos2w35Solution9 cos4 w 30cos2 w 35 0 let cos w

9cos^4w-30cos^2w+35

Solution

9 cos^4 w - 30cos^2 w + 35 = 0

let cos w = y

equation becomes

9y^4 - 30y^2 + 35 = 0

on solving we get

y = sqrt ( 5+ i sqrt 10) / 3 , sqrt ( 5- i sqrt 10) / 3 , - sqrt ( 5+ i sqrt 10) / 3 , - sqrt ( 5- i sqrt 10) / 3

or

cos w = sqrt ( 5+ i sqrt 10) / 3 , sqrt ( 5- i sqrt 10) / 3 , - sqrt ( 5+ i sqrt 10) / 3 , - sqrt ( 5- i sqrt 10) / 3

since all the solutions are imaginary

there will be no solutions for this equation