Show that `4sin27^0=(5+sqrt(5))^(1/2)-(3-sqrt(5))^(1/2)`

Prove that (1)cos36^(@)cos72^(@)cos108^(@)cos144^(@)=(1)/(16)(2) Show that 4sin27^(@)=sqrt(5+sqrt(5))-sqrt(3-sqrt(5))

(iii) ((sqrt(2))/(5))^(8)-:((sqrt(2))/(5))^(1/3)

Prove that: i) sin^(-1)(1/sqrt(5))+sin^(-1)(2/sqrt(5))=pi/2

cot((sin^(-1)1)/(sqrt(5))+(sin^(-4)2)/(sqrt(5)))

Prove that: sin36^(0)=(sqrt(10-2sqrt(5)))/(4)

4 sin 27^(0)= 1) sqrt(5+sqrt(5))+sqrt(3-sqrt(5)) 2) sqrt(5-sqrt(5))+sqrt(3+sqrt(5) 3) sqrt(5+sqrt(5))-sqrt(3-sqrt(5)) 4) sqrt(5+sqrt(5))+sqrt(3+sqrt(5)

( Show that: )/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5

which of the following is /are correct? (A) cos72^(0)=(sqrt(5)-1)/(4) (B) sin54^(0)=(sqrt(5)-1)/(4) (C) cot7(1)/(2)^(0)=sqrt(2)+sqrt(3)+sqrt(4)+sqrt(6) (D) 4sin27^(0)=sqrt(5+sqrt(5))+sqrt(3-sqrt(5))

Show that (1)/(sqrt(2)+sqrt(3))-(2)/(sqrt(5)-sqrt(3))+(3)/(sqrt(5)-sqrt(2))=0 .

The value of cos48cos12 (A) (sqrt(5)+3)/(8) (B) (3-sqrt(5))/(2) (C) (sqrt(5)+1)/(4) (D) (sqrt(5)-1)/(4)