Mark M. answered • 07/25/19

Retired Math prof with teaching and tutoring experience in trig.

tan(x - π/4) = (tanx - tanπ/4) / (1 + tanxtanπ/4))

(tanx - 1) / (1 + tanx)

since sinx = 7/25 and x is in quadrant 1, cosx = √[1 - sin^{2}x] = 24/25

So, tanx = sinx / cosx = 7/24

Therefore, tan(x - π/4) = (7/24 - 1) / (1 + 7/24) = (-17/24) / (31/24) = -17/31