Find the exact value cot7pi4 sec7pi4Solution1 cot 74 cot 2

Find the exact value

cot(7pi/4)

sec(7pi/4)

Solution

1)

cot (7/4) = cot (2 - /4)

cot (2 - A) = - cot (A)

cot (7/4) = - cot (/4) = - cos (/4) / sin (/4) = -1

2)

sec(7/4) = 1/ cos(7/4)

cos (2 - A) = cos (A)

cos (2 - /4) = cos (/4) = 1/2

sec(7/4) = = 1/ cos(7/4) = = 1/ cos(/4) = 2