Question

Please help me! I don’t need a long explanation

Answer 1

-
`\frac{\sqrt{2-√(2) } }{2}`

Explanation:

Note that
`(5\pi )/(8)` is in the second quadrant

where cos < 0 , hence overall sign will be negative

Using the half- angle formula

cos
`(5\pi )/(8)`

= -
`\sqrt{(1+cos(5\pi )/(4) )/(2) }`

= -
`\sqrt{(1-(√(2) )/(2) )/(2) }`

= -
`\sqrt{(2-√(2) )/(4) }`

= -
`\frac{\sqrt{2-√(2) } }{2}`