Question

if cos x =1/5 , then what is the positive value of tan 1/2x, in simplest radical form with a rational denominator?

Answer 1

Explanation:

sin(x)=sqrt(24)/5=2*sqrt(6)/5

tan(x/2)=sin(x)/(1+cos(x))

Thus, tan(x/2)=sqrt(6)/3

Answer 2

Answer: the positive value of tan(1/2x) in simplest radical form with a rational denominator is √(2/3).

Explanation:

Using the half-angle formula for tangent, we have:

tan(1/2x) = ±√((1-cos(x))/(1+cos(x)))

Substituting cos(x) = 1/5, we get:

tan(1/2x) = ±√((1-1/5)/(1+1/5))

= ±√(4/6)

= ±√(2/3)

Since we are looking for the positive value, we have:

tan(1/2x) = √(2/3)

Therefore, the positive value of tan(1/2x) in simplest radical form with a rational denominator is √(2/3).