Question

Urgent help please please please❤️Urgent​

Answer 1

Explanation:

Remember:

`cos(2A)=cos(A+A)=cos^2(A)-sin^2(A)=2cos^2(A)-1\\\\cos^2(A)=(cos(2A)+1)/(2) \\\\cos(A)=\pm\sqrt{(cos(2A)+1)/(2)} \\\\`

`cos ((A)/(2) )=\pm\sqrt{(1+cos(A))/(2) } \ with \left\{\begin{array}{c} \ +:\ if (A)/(2) \ is\ in\ I\ or\ IV\ quadran\\\ -:\ if (A)/(2) \ is\ in\ II\ or\ III\ quadran\\\end{array}\right.`

`cos(\pi)=-1\\\\cos((\pi)/(2) )=+\sqrt{(1+(-1))/(2)} =0\\\\cos((\pi)/(4) )=+\sqrt{(1+0))/(2)} =(√(2) )/(2) \\`

`cos((\pi)/(8) )=\sqrt{(1+(√(2))/(2)))/(2)} =\sqrt{(1)/(2) +(√(2) )/(4) }=(1)/(2) \sqrt{2+√(2) } \\\\\\cos((\pi)/(16) )=\sqrt{\frac{1+(1)/(2)*\sqrt{2+√(2) } }{2}}\\\\\\=\sqrt{(1)/(2) +(1)/(4)*\sqrt{2+√(2) } } \\\\\\=(1)/(2)*\sqrt{2+\sqrt{2+√(2) } } \\\\`