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# 2 cos x= sin x+1

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2 cos x= sin x+1

Guest Nov 4, 2014

#1
+26399
+5

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.

.

Alan  Nov 4, 2014
Sort:

#1
+26399
+5

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.

.

Alan  Nov 4, 2014

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