Solve the equation 2cos2x + 4sinx = 3.
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Tushar Chandra
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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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