Question

Sin^2x - 0,5sin2x= 0

Answer 1

Sinˇx -0,5.2.sinx.cosx = sin x(sin x-cosx)=0
a)sin x=0, x=k.pí
b)sinx-cosx=0, sinx=cosx
   x=pí/4+2k.pí
   x=5pí/4+2k.pí

Answer 2

We can solve this equation using the trigonometric identity sin(2x) = 2sin(x)cos(x).

Substitute sin(2x) with 2sin(x)cos(x) in the given equation:

sin^2(x) - 0.5(2sin(x)cos(x)) = 0

Simplify by factoring out sin(x):

sin(x)(sin(x) - cos(x)) = 0

This equation is satisfied when sin(x) = 0 or sin(x) - cos(x) = 0.

If sin(x) = 0, then x = nπ, where n is an integer.

If sin(x) - cos(x) = 0, then sin(x) = cos(x), which implies tan(x) = 1. So, x = π/4 + nπ, where n is an integer.

Therefore, the solutions to the equation sin^2(x) - 0.5sin(2x) = 0 are:

x = nπ or x = π/4 + nπ, where n is an integer.