Must do All parts Must use exact values no decimals A Show t

Must do All parts. Must use exact values (no decimals). A. Show the exact value of cos(90 degree)-0 using the double angle identity. B. Show the exact value of sin(90 degree)-1 using a sum/difference identity. C. Find the exact value of cos (105 degree) using the sum/difference identity. D. Find the exact value of cos 112.5 degree using the half-angle identity.

Solution

A . cos90= cos 2(45) =2 cos²45-1=2(1/2)-1=1-1=0

B. sin 90= sin(45 + 45) = sin 45 cos 45 + cos 45 sin 45=(1/sqrt2)(1/sqrt2)+(1/sqrt2)(1/sqrt2)=(1/2)+(1/2)=1

C.cos 105=cos(60+45)=cos 60 cos 45-sin60sin 45=(1/2)(sqrt2/2)-(sqrt3/2)(sqrt2/2)=sqrt2(1-sqrt3)/4