2 cos x= sin x+1

Square both sides:

4cos²x = sin²x + 2sinx + 1

 

Replace cos² by 1 - sin²

4(1 - sin²x) = sin²x + 2sinx + 1

 

Collect terms

5sin²x + 2sinx - 3 = 0

 

This can be written as

(sinx + 5/5)(sinx - 3/5) = 0  or (sinx + 1)(sinx - 3/5) = 0

 

So sinx = -1 and sinx = 3/5

This means x = asin(-1) = 3pi/2 (=270°)

and x = asin(3/5) ≈ 36.87°

 

Adding and subtracting multiples of 2pi (360°) to these also satisfies the original equation.

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