cos5π6=−√32=2cos25π12−1=1−2sin25π12{cos25π12=2−√34sin25π12=2+√34⇒{cos5π12=√3−12√2sin5π12=√3+12√2
2√2cos(5π12−x)=2√2cos5π12cosx+2√2sin5π12sinx
=(√3−1)cosx+(√3+1)sinxVế trái =(√3−1)cosx.sinx+(√3+1)sin2x=1
⇒√3−12sin2x+√3+12(1−cos2x)=1
⇒√3−12sin2x−√3+12cos2x=1−√32
⇒cos5π12sin2x−sin5π12cos2x=−cos5π12
⇒sin(5π12−2x)=cos5π12=sinπ12
⇒5π12−2x=π12+2kπ hoặc 5π12−2x=11π12+2kπ
⇒x=π6−kπ,−π4−kπ