[cos105⁰(cos277⁰sin172⁰-cos7⁰sin82⁰]/(2√2)⁻²==(2√2)²·cos105⁰·[1/2(sin(172⁰-277⁰)+sin(172⁰+277⁰))-1/2(sin(82⁰-7⁰)+sin(82⁰+7⁰))]==4·2·1/2·cos105⁰·(sin(-105⁰)+sin449⁰-sin75⁰-sin89⁰)==4·cos105⁰·(-sin105⁰+sin(2π+89⁰)-sin75⁰-sin89⁰)==-4·cos105⁰·sin105⁰-4·cos105⁰·sin75⁰==-2·sin210⁰-4·1/2·(sin(75⁰-105⁰)+sin(75⁰+105⁰)==-2sin(π+30⁰)-2[(sin(-30⁰)+sin180⁰)]==-2(-sin30⁰)-2[(-sin30⁰)+0]=2sin30⁰+2sin30⁰=4sin30⁰=4·(1/2)=2