Prove that, `15_(C_2) =105`

With usual notations prove that C_1/C_0 + 2. C_2/C_1 + 3.C_3/C_2 + ……+n.(C_n)/(C_(n-1)) = (n(n +1))/(2) Hence prove that (15C_1)/(15C_0) + 2.(15C_2)/(15C_1) + 3. (15C_3)/(15C_2) +……..+ 15. (15C_15)/(15C_14) = 120

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

Prove that: sin 105^@+cos 105^@=cos 45^@

Prove that: sin 105 ^(@) + cos 105 ^(@) = cos 45 ^(@)

Prove that cos(2pi)/(15)cos(4pi)/(15)cos(8pi)/(15)cos(14pi)/(15)=1/(16)

Prove that cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((14pi)/(15))=1/(16)

Prove that cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((16pi)/(15))=1/(16)

Prove that cos "" (2pi)/(15) cos "" (4pi)/(15) cos "" (8pi)/(15) cos "" (14pi)/(15) = (1)/(16).

Prove that (tan75^(@))/(cot15^(@))=1

Prove that sec^(2) (tan ^(-1) 3) + cosec^(2)(cot^(-1)2) = 15