Answer:
-4/6 or -2/3 simplified. You didn't write that as an answer, so I'm guessing -4/5 :]
Explanation:
To find the value of tan(x - π/4), we can use the tangent subtraction formula:
tan(x - π/4) = (tan(x) - tan(π/4)) / (1 + tan(x) * tan(π/4))
Given that tan(x) = 1/5, we can substitute this value into the formula:
tan(x - π/4) = (1/5 - tan(π/4)) / (1 + (1/5) * tan(π/4))
Now, let's calculate the value of tan(π/4):
tan(π/4) = 1
Substituting this value into the formula:
tan(x - π/4) = (1/5 - 1) / (1 + (1/5) * 1)
tan(x - π/4) = (1/5 - 1) / (1 + 1/5)
tan(x - π/4) = (-4/5) / (6/5)
Simplifying the fraction:
tan(x - π/4) = -4/6
Reducing the fraction:
tan(x - π/4) = -2/3
Therefore, tan(x - π/4) is equal to -2/3.
You're welcome!