Solving 1.732cos(x)-1.16=sin(x) for x

[saii]

Homework Statement

Find X?
1.732cos(x)-1.16=sin(x)

Answer: X = 24.6

Homework Equations

The Attempt at a Solution

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

1.732cos(x)-1.16=sqrt(1-cos(x)^2)
1.732^2 cos(x)^2 -1.16^2= 1-cos(x)^2
3cos(x)^2-2.3456=1-cos(x)^2
4cos(x)^2=3.3456
cos(x)^2=3.34556/4
x=23.8

There when wrong?

 

[CompuChip]

You squared both sides in the first step, right?
Well, the square of 1.732cos(x)-1.16 is not 1.732^2 cos(x)^2 -1.16^2.
You can check it: (a - b)² is not a² - b² but (a - b)(a - b), then open up the brackets...

 

[saii]

ok thx.. mean i can use (a-b)^2=a^2-2ab+b^2?