Question

Помогите решить 712 номер.

Answer 1

$1)8Sin15^{0}*Cos15^{0}=4*2Sin15^{0}*Cos15^{0}=4*Sin30^{0}=4*\frac{1}{2}=\boxed2\\\\2)4Sin22^{0}30'*Cos22^{0} 30'=2*2Sin22^{0}30'*Cos22^{0} 30'=\\\\=2Sin(2*22^{0}30')=2Sin45^{0}=2*\frac{\sqrt{2} }{2}=\boxed{\sqrt{2}} \\\\3)Sin15^{0}*Cos15^{0}=0,5*2Sin15^{0} Cos15^{0} =0,5*Sin30^{0}=0,5*0,5=\boxed{0,25} \\\\4)Sin^{2}15^{0}-Cos^{2}15^{0}=-(Cos^{2}15^{0}-Sin^{2}15^{0})=-Cos(2*15^{0})=\\\\=-Cos30^{0}=\boxed{-\frac{\sqrt{3}}{2}}$

$5)\sqrt{2}(Cos^{2}22,5^{0}-Sin^{2}22,5^{0} )=\sqrt{2}Cos(2*22,5^{0})=\sqrt{2}Cos45^{0}=\\\\=\sqrt{2} *\frac{\sqrt{2} }{2}=\boxed1 \\\\6)2tg15^{0}:(1-tg^{2}15^{0})=\frac{2tg15^{0} }{1-tg^{2}15^{0}}=tg(2*15^{0})=tg30^{0}=\boxed{\frac{\sqrt{3} }{3}}$