1/4tan(2x)
sin2x/4cos2x
To simplify the expression 1/4tan(2x), we can start by rewriting it using the identity tan(2x) = 2tan(x)/(1 - tan^2(x)).
1/4tan(2x) = 1 / [4 * (2tan(x)/(1 - tan^2(x)))]
Next, we'll simplify the expression further:
1 / [4 * (2tan(x)/(1 - tan^2(x)))]
To simplify the expression in the denominator, we can use the identity 1 - tan^2(x) = sec^2(x):
1 / [4 * (2tan(x)/(sec^2(x)))]
Now, we can simplify it by multiplying the numerators and denominators:
1 * sec^2(x) / [4 * (2tan(x))]
This can be further simplified by canceling out the common factor of 2:
sec^2(x) / (8tan(x))
Therefore, the simplified expression is sec^2(x) / (8tan(x)).
To simplify the expression 1/4tan(2x), we can use the trigonometric identity for tangent:
tan(2x) = 2tan(x) / (1 - tan^2(x))
Substituting this into the expression:
1/4tan(2x) = 1/4 * (2tan(x) / (1 - tan^2(x)))
Next, we'll simplify the expression further by multiplying the numerators:
1/4 * 2tan(x) = 2/4 * tan(x) = 1/2 * tan(x)
Therefore, the simplified expression is 1/2 * tan(x).