what does sin2x/cos2x equal to?
To find the value of sin(2x)/cos(2x), we can use one of the trigonometric identities known as the tangent identity.
The tangent identity states that tan(x) = sin(x)/cos(x). We can rewrite sin(2x)/cos(2x) using this identity.
First, let's express sin(2x) and cos(2x) in terms of sin(x) and cos(x) using a double-angle formula:
sin(2x) = 2sin(x)cos(x)
cos(2x) = cos^2(x) - sin^2(x)
Now, substitute these expressions into sin(2x)/cos(2x):
sin(2x)/cos(2x) = (2sin(x)cos(x))/(cos^2(x) - sin^2(x))
We can simplify the expression further by canceling out common factors. In particular, notice that sin(x) and cos(x) appear in both the numerator and denominator, so they can be canceled out:
sin(2x)/cos(2x) = 2tan(x)/(1 - tan^2(x))
So, sin(2x)/cos(2x) is equal to 2tan(x)/(1 - tan^2(x)).