4cos^2(theta)+2sin(theta)=2

Answer:The value of given expression i.e Ф is 90°  and - 30° Step-by-step explanation:Given as :4 cos²Ф + 2 sinФ = 2 ∵  sin²Ф +  cos²Ф = 1  ,  so ,  cos²Ф = 1 -  sin²ФOr, 4 ( 1 - sin²Ф ) + 2 sinФ = 2 Or, 4 - 4 sin²Ф + 2 sinФ = 2 or, 4 sin²Ф - 2 sinФ - 4 + 2 = 0or, 4 sin²Ф - 2 sinФ - 2 = 0or, 2 sin²Ф -  sinФ - 1 = 0or, 2 sin²Ф - 2 sinФ +  sinФ - 1 = 0Or, 2 sinФ ( sinФ - 1 ) + 1 ( sinФ - 1 ) = 0∴  ( sinФ - 1 ) ( 2 sinФ + 1 ) = 0i.e  ( sinФ - 1 ) = 0  And  ( 2 sinФ + 1 ) = 0since   ( sinФ - 1 ) = 0  So, sinФ  = 1Or,  Ф = [tex]sin^{-1}(1)[/tex] = 90° And ( 2 sinФ + 1 ) = 0Or,  2 sinФ = - 1Or,  sinФ = - [tex]\frac{1}{2}[/tex]Or,   Ф = [tex]sin^{-1}(-\frac{1}{2})[/tex] = - 30° Hence the value of given expression i.e Ф is 90°  and - 30°    Answer