" 69.gos "(11 pi)/(6)" an "477" and "(4)/(8)?

cos((11 pi)/(6))=

cos((11 pi)/(6))=

Prove that (i) " tan"^(2) .(pi)/(3) + 2cos^(2) .(pi)/(4)+ 3 sec^(2).(pi)/(6)+ 4 cos^(2).(pi)/(2)=8 (ii) " sin ".(pi)/(6) " cos 0 + sin ".(pi)/(4) " cos " .(pi)(4) + " sin " .(pi)/(3) "cos " .(pi)/(6) =(7)/(4) (iii) " 4sin " (pi)/(6) " sin"^(2) (pi)/(3) + 3 " cos " .(pi)/(3) " tan ".(pi)/(4) = " cosec"^(2).(pi)/(2)=4

The numbers tan (-(11pi)/(6)), tan((21pi)/(4))and cot ((283pi)/(6)) are in-

(tan) (11 pi) / (3) (- 2sin) (4 pi) / (6) - (3) / (4) (cos ec ^ (2)) (pi) / (4) + (4cos ^ (2)) (17 pi) / (6) = (3-4sqrt (3)) / (2)

One of the value of ("cos"(pi)/(6) +i "sin"(pi)/(6))^((1)/(2)) + ("cos"(pi)/(6)- i "sin"(pi)/(6))^((11)/(2)) is

cos ((pi) / (11)) cos (2 (pi) / (11)) cos (3 (pi) / (11)) cos (4 (pi) / (11)) cos (5 (pi) / (11))