To simplify the expression 1 - sin^2(x) on the left side of the equation, we can use the Pythagorean identity sin^2(x) + cos^2(x) = 1:
1 - sin^2(x) = cos^2(x)
Now we have:
cos^2(x) = sin(2x) / cos(x)
Using the double-angle identity sin(2x) = 2sin(x)cos(x), we get:
cos^2(x) = 2sin(x)cos(x) / cos(x)
Simplifying this expression further by canceling out the cos(x) terms on both sides, we have:
cos(x) = 2sin(x)
Therefore, the simplified equation is cos(x) = 2sin(x).
To simplify the expression 1 - sin^2(x) on the left side of the equation, we can use the Pythagorean identity sin^2(x) + cos^2(x) = 1:
1 - sin^2(x) = cos^2(x)
Now we have:
cos^2(x) = sin(2x) / cos(x)
Using the double-angle identity sin(2x) = 2sin(x)cos(x), we get:
cos^2(x) = 2sin(x)cos(x) / cos(x)
Simplifying this expression further by canceling out the cos(x) terms on both sides, we have:
cos(x) = 2sin(x)
Therefore, the simplified equation is cos(x) = 2sin(x).