Question

If tan x = 1/5, what is tan (x-(pi/4))
-4/5
6/5
3/2
-3/2

Answer 1

-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!