Solve the equation 2cos2x + 4sinx = 3.  

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to solve 2*cos 2x + 4*sin x = 3.

We use the relation: cos 2x = 1 – 2* (sin x)^2

2*cos 2x + 4*sin x = 3

=> 2* (1 – 2* (sin x)^2) + 4*sin x = 3

=> 2 – 4*(sin x)^2 + 4* sin x = 3

let y = sin x

=> 4y^2 – 4y + 1 = 0

=> (2y – 1)^2 = 0

=> 2y = 1

=> y = 1/2

As y = sin x , sin x = 1/2 or x = arc sin (1/2) = pi/6 + 2*n*pi and x = 5*pi/6 + 2*n*pi

We get x = pi/6 + 2*n*pi and x = 5*pi/6 + 2*n*pi.

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