Question Number 101107 by PengagumRahasiamu last updated on 30/Jun/20

Commented byDwaipayan Shikari last updated on 30/Jun/20

sin6°−sin66°+sin78°−sin42°  =−2cos36°sin30°+2cos60°sin18°  =sin18°−cos36°=(((√5)−1)/4)−(((√5)+1)/4)=−(1/2)     (/)

Commented byDwaipayan Shikari last updated on 01/Jul/20

((sin66°−sin6°)/(sin6°sin66°))+(1/(sin78°))−(1/(sin42°))  =((2cos36°sin30°)/(sin6°sin66°))+((sin42°−sin78°)/(sin78°sin42°))  =((cos36°)/(sin6°sin66°))−((sin18°)/(sin78sin42))  =((2cos36°)/(cos60°−cos72°))−((2sin18°)/(cos36−cos120°))    =((((√5)+1)/2)/((1/2)−(((√5)−1)/4)))+((((√5)−1)/2)/((1/2)−(((√5)+1)/4))) =8    (you will get youranswer after simplifying)

Answered by Ar Brandon last updated on 30/Jun/20

a\S=sin6°−sin42°−sin66°+sin78°          =(sin6°−sin66°)+(sin78°−sin42°)          =−2cos36°sin30°+2cos60°sin18°          =sin18°−cos36°=(((√5)−1)/4)−(((√5)+1)/4)=−(1/2)

Answered by Ar Brandon last updated on 30/Jun/20

b\T=(1/(sin6°))−(1/(sin66°))+(1/(sin78°))−(1/(sin42°))=((sin66°−sin6°)/(sin66°sin6°))+((sin42°−sin78°)/(sin42°sin78°))           =((2cos36°sin30°)/(((−1)/2)(cos72°−cos60°)))+((−2cos60°sin18°)/(((−1)/2)(cos120°−cos36°)))           =((−2cos36°)/((sin18°−(1/2))))+((2sin18°)/((−(1/2)−cos36°)))=((−2∙((((√5)+1))/4))/(((((√5)−1)/4)−(1/2))))+((2∙(((√5)−1)/4))/((((−1)/2)−(((√5)+1)/4))))           =((−2((√5)+1))/((√5)−1−2))+((2((√5)−1))/((−2−(√5)−1)))=((2((√5)+1))/(3−(√5)))+((2(1−(√5)))/(3+(√5)))           =((2[(1+(√5))(3+(√5))+(1−(√5))(3−(√5))])/((3−(√5))(3+(√5))))=((2(8+4(√5)+8−4(√5)))/4)  (1/(sin6°))−(1/(sin66°))+(1/(sin78°))−(1/(sin42°))=8

Commented byPengagumRahasiamu last updated on 30/Jun/20

Thank you, Sir 🙏🏻

Commented byAr Brandon last updated on 30/Jun/20

You're welcome mate ! 😃