Please explain I am confused thank you

Step-by-step explanation:

You have to use the half angle identities for trig.  You will also need access to a unit circle with radian measures of angles.  The identity for the half angle for sin is

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To use a half angle identity, the trick is to rewrite the half angle so that when you bring up that 2 in the denominator and flip it to multiply you get back the angle you started with.  Our angle is 7π/8.  Divide the 8 by 2 and you get your angle to be in the form

Note that when you bring up the 2 and flip it to multiply you get back 7π/8.

Do you see that?  For the formula, then, our angle theta is 7π/4.  If you look to the unit circle, you see that the cosine of that angle is √2/2.  Filling in the formula:

Get a common denominator up on top there and simplify:

You'll bring up that bottom 2 and flip it to multiply:

Simplify to get

Since 4 is a perfect square, the final simplification will be to pull it out as a 2:

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And you're all done!  Easy if you know how to use the formula and the unit circle.