Question

If sin ⁡x= 7/25, and 0 <x< π/2, what is tan⁡(x − π/4)?

I don't get how to do this. We're talking about the "Difference Identity for Tangent". If you could help I'd really appreciate it.

Answer 1

since sinx = 7/25
cosx = 24/25
tanx = 7/24

tan(x - π/4) = (tanx - tan π/4)/(1 + tanx tan(π/4))
= (7/24 - 1)/(1 + 7/24 * 1) = -17/31

makes sense, since x < π/4, x-π/4 is negative