solve the following trigonometric equation Solve the followi

solve the following trigonometric equation

Solve the following trigonometric equation 4 cos^2 x = 7cosx + 2,0 x lessthenorequalto x lessthenorequalto 180degree

Solution

let cos x = y

therefore ,

4y^2 = 7y + 2

4y^2 - 7y - 2 = 0

solving the quadratic equatio we get

y = 2

y = -1/4

or cos x = 2

cos x = -1/4 , x = 2pi*n - cos^-1 (-1/4) , x = 2pi*n + cos^-1(-1/4)

solutions

x = cos^-1 (-1/4)