Find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas. sec u = −2, π/2 < u < π

now... we have -2/1   but... which one is the negative?   well
we know the angle is " π/2 < u < π", that simply means, the 2nd quadrant
well, in the 2nd quadrant, the "x" or adjacent side is negative, so the adjacent side is then -1

now, let us use the pythagorean theorem, to get the opposite side



now..which one though?  well, recall, we're in the 2nd quadrant, in the 2nd quadrant "y" or the opposite side, is positive, so is √(3) then

now... let's plug in those values in the double-angle identities then





simplify away

put like terms together.orremember that the 45 becomes negative when moved to the other side.orthe minuses cancel out.