2sin72×sin306/cot18×sin15=2sin 72×sin(360-54)/(cos18/sin18)×sin(180-30)
= 2sin72×(-sin54)/(sin72/sin18)×sin30
= -2sin72sin54/(sin72/2sin18)
= -2sin72sin54×2sin18/sin72
= -4sin54×sin18
= -4(1+√5 /4)(-1+√5 /4)
= -4/16(1+√5)(-1+√5)
= -1/4(√5+1)(√5-1)
= -1/4((√5)²-1²)
= -1/4(5-1)
= -1
" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
2sin72×sin306/cot18×sin15=2sin 72×sin(360-54)/(cos18/sin18)×sin(180-30)
= 2sin72×(-sin54)/(sin72/sin18)×sin30
= -2sin72sin54/(sin72/2sin18)
= -2sin72sin54×2sin18/sin72
= -4sin54×sin18
= -4(1+√5 /4)(-1+√5 /4)
= -4/16(1+√5)(-1+√5)
= -1/4(√5+1)(√5-1)
= -1/4((√5)²-1²)
= -1/4(5-1)
= -1