Find an equation of the tangent line to the curve at the given point.
y = tan x at point (pi/4,1)
The Attempt at a Solution
step 1. find the derivative of tan x, which sec^2 x
step 2. find the slope.
this is where I mess up. I assume that I have to square x where sec is pi/4. Sec^2 of pi/4 I think would be the hypotenuse/x which is 1/2√2. So I square that, which to me would be 1/ (4*2) or 1/8. But the solution manual says it's the square of 2√2. why? Obviously I don't know how to square secant.
step 3. insert the slope into the y - y = m(x - x) formula, which I can do.
In the solution manual below, they don't have negative signs, so there's a few negative signs missing but I know where they are.