Prove that the average of the numbers `n sin n^@`, `n = 2,4,6...180` is `cot 1^@`

The arithmetic mean of the numbers 2s in2^0,4sin4^0,6sin^0, ddot, 178s in 178^0,180sin180^0 is sin1^0 b. "tan"1^0 c. cot1^0 d. t a n 89^0

The arithmetic mean of the numbers 2sin2^(@), 4sin4^(@), 6 sin 6^(@), …………. 178 sin 178^(@), 180 sin 180^(@)

Prove that ((n + 1)/(2))^(n) gt n!

Prove that 2 sin 2^(@)+4sin 4^(@)+6sin 6^(@)+........+180sin 180^(@)=90 cot 1^(@) .

Prove that n! (n+2) = n! +(n+1)! .

Prove that t a n A+2t a n2A+4t a n4A+8cot8A=cot Adot

Prove that: n !(n+2)=n !+(n+1)!

The average of n numbers x_(1),x_(2),x_(3),..,x_(n) is M. If x_(n) is replaced by x', then new average is

Prove that [(n+1)//2]^n >(n !)dot

prove that 2+4+6+…2n=n^(2)+n , for all natural numbers n.