Prove that
`(i) " 2sin " (5pi)/(12) " sin " (pi)/(12)=(1)/(2)`
`(ii) " 2 cos " (5pi)/(12) " cos " .(pi)/(12)=(1)/(2)`
`(iii) " 2 sin ".(5pi)/(12) " cos " (pi)/(2) = ((2+sqrt(3))/(2))`

Evaluate : (i) " sin " (pi)/(2) " "(ii) " sin " (5pi)/(12)

Prove that (i) "sin " (7pi)/(12) " cos " (pi)/(2) - "cos " *(7pi)/(12) " sin " (pi)/(4) = (sqrt(3))/(2) (ii) " sin " (pi)/(4) " cos " (pi)/(2) + "cos"(pi)/(4) " sin " (pi)/(12) = (sqrt(3))/(2) (iii) " cos " (2pi)/(3) " cos " (pi)/(4) - " sin " (2pi)/(3) " sin " (pi)/(4) =(-(sqrt(3) +1))/(2sqrt(2))

Prove that; 2(sin(5 pi))/(12)(sin pi)/(12)=(1)/(2)

Prove that 2sin((5 pi)/(12))cos((pi)/(12))=(2+sqrt(3))/(2)

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

Evaluate : cos ^(2) ""(pi)/(12) - sin ^(2) ""(pi)/(12)

"sin" pi/12 "sin" (5pi)/12=

2sin((5 pi)/(12))(sin((pi)/(12)))=

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

Prove that; 2sin((5pi)/12)sin(pi/12)=1/2