Question

Rewite uravnenie  1-cos2x=2sinx    

Answer 1

1-cos2x=2sinx

1-(cos^2x-sin^2x)=2sinx

sin^2x+cos^2x-cos^2x+sin^2x-2sinx=0

2sin^2x-2sinx=0

2sinx(2sinx-1)=0

2sinx=0

2sinx=Пn

sinx=Пn/2

2sinx-1=0

2sinx=1

sinx=1/2

x=(-1)^n*arcsin(1/2)+Пn

x=(-1)^n*П/6+Пn

 

Answer 2

To rewrite the equation "1 - cos(2x) = 2sin(x)", we can use trigonometric identities to simplify it. Here's the step-by-step process:

Step 1: Expand the double-angle identity for cosine. 1 - (cos²(x) - sin²(x)) = 2sin(x)

Step 2: Simplify the expression by removing the parentheses. 1 - cos²(x) + sin²(x) = 2sin(x)

Step 3: Combine like terms on the left-hand side. (1 - cos²(x) + sin²(x)) = 2sin(x)

Step 4: Replace sin²(x) with 1 - cos²(x) using the Pythagorean identity. (1 - cos²(x) + (1 - cos²(x))) = 2sin(x)

Step 5: Simplify the expression further. 2 - 2cos²(x) = 2sin(x)

Step 6: Divide both sides by 2 to simplify the equation. 1 - cos²(x) = sin(x)

So the rewritten equation is "1 - cos²(x) = sin(x)".