Question

Find the exact value without a calculator cos π\8= cos π/4/2​

Answer 1

Answer:

Step-by-step explanation:

1+cos 2a=2cos^2a

cos a=√[(1+cos 2a)/2]

$put~a=\frac{\pi }{8} \\2a=\frac{\pi }{4} \\\\cos\frac{\pi }{8} =\sqrt{\frac{1+cos \frac{\pi }{4} }{2} } \\=\sqrt{\frac{1+\frac{\sqrt{2}}{2} }{2} }\\=\frac{\sqrt{2+\sqrt{2}}}{2}$