Solve: Cos(Sec^-1 u)
Recall that sec is 1/cos
Suppose to make this a little easier to understand that the problem
says sec^-1(2), which means u = 2 . So we want the angle which has a
sec value equal to 2. That is the same as saying 1/cos = 2 which means
cos = 1/2
Cos is 1/2in the first quadrant 60 degrees
That gives us cos(60) which we know is 1/2 and 1/2 = 1/u.
Therefore the answer is simply 1/u. That makes logical sense too since sec = 1/cos and cos = 1/sec. They are inverses.
You can also do this by labeling parts of the right triangle. You
know that sec^-1 u means that the adjacent side of the right triangle
is 1 and the hypotenuse is u, since sec = hypotenuse/adjacent.
Therefore cos of the angle equal 1/u