Answer: sqrt(2)
Explanation:
Remember that sec x = 1/cos x.
That means that sec 7pi/4 = 1/cos(7pi/4)
cos(7pi/4) = -cos(7pi/4 - pi)
= -cos(3pi/4)
cos(3pi/4) is a special angle which evaluates to -sqrt(2)/2.
Hence, -cos(3pi/4) evaluates to simply sqrt(2)/2
Since cos(7pi/4) is equal to -cos(3pi/4),
cos(7pi/4) is equal to sqrt(2)/2.
Lastly, sec 7pi/4 = 1/cos(7pi/4) , which is the reciprocal of sqrt(2)/2, that is 2/sqrt(2).
Rationalizing the answer 2/sqrt(2) gives sqrt(2)