prove that :`sin((5pi)/18)-cos((4pi)/9)=sqrt(3)sin(pi/9)`

Prove that: i) sin(5pi)/(18) - cos(4pi)/(9) = sqrt(3)sinpi/9 ii) cos(3pi)/4+A-cos((3pi)/(4)-A)=-sqrt(2)sinA

Prove that 2sin((5pi)/12)cos(pi/12)=(2+sqrt3)/2

Prove that: sin(pi/10). cos(pi/5)=1/4

Prove that: cos(pi/10)-sin(pi/10)=sqrt(2)sin((3pi)/(20))

prove that : cos(pi/12)-sin(pi/12)=1/(sqrt(2))

Prove that: sin(pi/5)sin( (2pi)/5)sin(3pi/5)sin(4pi/5)=5/(16)

Prove that: 15sin(5pi)/(12)+15cos(5pi)/(12)-20sin^3(5pi)/(12)-20cos(5pi)/(12)=0

Prove that: sin((4pi)/9+7)cos(pi/9+7)-cos((4pi)/9+7)sin("pi/9+7)=(sqrt(3))/2

Prove that: sin(pi/14)sin((3pi)/14)sin((5pi)/14)sin((7pi)/14)sin((9pi)/14)sin((11pi)/14)sin((13pi)/14)=1/(64)

Prove that: sin((3pi)/8-5)cos( pi/8+5)+cos((3pi)/8-5)sin(pi/8+5)=1