+0  
 
0
338
1
avatar

2 cos x= sin x+1

Guest Nov 4, 2014

Best Answer 

 #1
avatar+26640 
+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+0 Answers

 #1
avatar+26640 
+5
Best Answer

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

28 Online Users

avatar
avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details