Prove that `4(cos66^(@)+sin84^(@))=sqrt(3)+sqrt(15)`

Prove that cos 15 ^(@) - sin 15^(@) = (1)/(sqrt2)

Prove that sin20^(@)sin40^(@)sin80^(@)=(sqrt(3))/(8)

4(sin2 4^0+cos6^0)=sqrt(3)+sqrt(15)

Prove that cos^(-1) (sqrt(1/3))-cos^(-1) (sqrt((1)/(6)))+cos^(-1) ((sqrt(10)-1)/(3sqrt2))=cos^(-1) (2/3)

Prove that ; 4 sin 27^@=(5+sqrt(5))-sqrt((3-sqrt(5))) we have

Prove that sin 36^(@) + cos 36^(@) = sqrt(2) cos 9^(@)

Prove that sin 20^(@) sin 40^(@) sin 80^(@) = (sqrt3)/(8).

Prove that: cos^2 45^0-sin^2 15^0=(sqrt(3))/4

(a) Prove that sin65^(@)+cos65^(@)=sqrt(2)cos 20^(@) (b) Prove that sin47^(@)+cos77^(@)=cos17^(@)

Prove that: (a) cos510^(@) sin510^(@) + sin(-330^(@)) cos(-390^(@))=0 b) tan(11pi)/(3) -2sin(9pi)/3-3/4"cosec"^(2)pi/4 + 4cos^(2)(17pi)/6=(3-2sqrt(3))/2