sin^2 x +sin2x = 0.25

Question

sin 2

Answer 1

Convert all the arguments to an angle of 2x. Thus sin square is now (1-cos2x)/2 using the half -angle formulas.

sin2x is also converted to the sqare root of an expression containing cos 2x

 

You have now an equation only with cos 2x to wit:

 

(1-cos 2x)/2  + sqrt (1 - cos² 2x) =0.5

 

This is easy to convert to an equation of the second degree.

The solution of this equation will give you the value of cos2x. From there you can easily find x and sinx.

 

The solution is: sinx = 0.1188

Answer 2

I would suggest that you graph this as a function first.  You will see that there are multiple solutions, one of which is x = .119067.