if chord y=mx+1 of the circle x^2+y^2=1 subtends an angle 45 degrees at the major segment of the circle,then the value of m is
1. I'm not sure that I understand your question correctly(?).
2. Draw a sketch.
3. The perpendicular bisector of the chord has the slope $\displaystyle n = -\frac1m$ which correspond to an angle of 67.5° to the x-axis.
4. The slope of the sekant correspond to an angle of -22.5° and therefore
$\displaystyle m = \tan(-22.5^\circ)$
5. Use some simple trig-properties to get
$\displaystyle \tan(-22.5^\circ) = 1-\sqrt{2}$