am going to use % as alpha sign
the parametric equations of the curve C are:
x = a tan %
y = a sec %
dy/dx = sin%
show that the equation of the tangent to C at pont P(a tan %, a sec %), where 0<%<(pie/2) is
y = x sin% + a cos%
y - y1 = m(x - x1) is the standard slope-point form of a line.
m is the gradient of the line. (x1, y1) is a known point on the line.
You're given a point on the tangent, so x1 and y1 are known. And you've got dy/dx = m. So sub the stuff you know into the above:
.
And I've already all but shown you that simplifies to .