#1**+5 **

Square both sides:

4cos^{2}x = sin^{2}x + 2sinx + 1

Replace cos^{2} by 1 - sin^{2}

4(1 - sin^{2}x) = sin^{2}x + 2sinx + 1

Collect terms

5sin^{2}x + 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

#1**+5 **

Best Answer

Square both sides:

4cos^{2}x = sin^{2}x + 2sinx + 1

Replace cos^{2} by 1 - sin^{2}

4(1 - sin^{2}x) = sin^{2}x + 2sinx + 1

Collect terms

5sin^{2}x + 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