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a=22,5°

sina=sin45°/2=√1-cos45°/2=√1-√2/2/2=√2-√2/2/2=√2-√2/4=√2-√2/2

cosa=cos45°/2=√1+cos45°/2=√1+√2/2/2=√2+√2/2/2=√2+√2/4=√2+√2/2

tga=tg45/2=√1-cos45/1cos45=√1-√2/2/1+√2/2=√2-√2/2+√2/2=√2-√2/2+√2=√(2-√2)²/(2+√2)92-√2)=2-√2/√4-2=(2-√2*√2/√2*√2=2(√2-1)/2=√2-1

a=67.5

sin135/2=√-cos135/2=1-(-√2/2)/2=1√2/2/2=√2+√2/2=√2√/4=√2+2/2

cos135/2=√1+cos135/2=√1(-√2/2)/2=1-√2/2/2=√2-√2/2/2=2-√2/4=2-√2/2

214

f(x)=√x-1  g(x)=√3-x

F=f+g={√ x-1+√3-x}

D(F)={√ x-1+√3-x}⇔{ x≥1, x≤3}⇒ D(F)=[1;3]

բ)F=f-g=√x-1-√3-x

D(F)={√ x-1+√3-x}⇔{ x≥1, x≤3}⇒ D(F)=[1;3]

գ)F=f*g=√ x-1*√3-x

D(F)={√ x-1*√3-x}⇔{ x≥1, x<3}⇒ D(F)=[1;3]

դ)F=f/g=√ x-1/√3-x

D(F)={x-1≥0, 3-x≥0, 3-x≠0⇔{ x≥1, x<3}⇒D(F)=[1;3]

215

f(x)=1+x² g(x)=1/1-x

F=fºg

F=1+(1/1-x)²=(1-x)²+1/(1-x)²=1-2x+x²+1/(1-x)²=x²-2x+2/(1-x)²