Question

Need help with this question please!!

Answer 1

`\displaystyle\\\tan x=1\\ 0^o<x<90^o\\\implies~x=\arctan(1)=45^o\\\\\sin\left((x)/(2)\right)=\sqrt{(1-\cos x)/(2)}\\\\\sin\left((45^o)/(2)\right)=\sqrt{(1-\cos 45^o)/(2)}\\\\\sin\left((45^o)/(2)\right)=\sqrt{(1-(√(2))/(2))/(2)}\\\\\sin\left((45^o)/(2)\right)=\sqrt{((2-√(2))/(2))/(2)}\\\\\sin\left((45^o)/(2)\right)=\sqrt{(2-√(2))/(4)}\\\\\sin\left((45^o)/(2)\right)=(1)/(2) \sqrt{2-√(2)}`

.

.