Using Tully Fisher to measure Distance Problem Can anyone explain by looking at the solution in the pic, how did the cos (i) came about?
I guess they are getting this from the major-minor axis info in the question, but I am not sure about the derivation.

Also v=300/sin(i), what is this formula?

Many thanks :)
With the Tully Fisher relation, the inclination angle is determined from the major-minor axis ratio where $sin(i) = \sqrt{1-q^2} $ and q is the inverse of your ratio. 

You need to apply the sine of the angle to the rotational velocity because the measure is based on our line of sight observation which must be converted to the true 3D velocity.