If `sum_(n=1)^nalpha_n=a n^2+b n ,w h e r ea ,b` are constants and `alpha_1,alpha_2,alpha_3 in {1,2,3,......,9}a n d25alpha_1,37alpha_2,49alpha_3` be three digit number, then prove that `|[alpha_1,alpha_2,alpha_3],[ 5, 7, 9],[ 25alpha_1, 37alpha_2, 49alpha_3]|=0`

If alpha Is the fifth root of unity, then, prove that : Log_2|1+alpha+alpha^(2)+alpha^(3)-(1/alpha)|=1

If alpha_1,alpha_2....alpha_(n-1) are the nth roots of unity then show that (5-alpha_1)(5-alpha_2)(5-alpha_3)...(5-alpha_(n-1))= (5^n-1)/4

If 1, alpha,alpha^2.......alpha^(n-1) are the nth roots of unity then prove that (1-alpha)(1-alpha^2).....(1-alpha^(n-1))=n

Prove that, tan 8alpha - tan 5 alpha - tan 3 alpha = tan 8alpha tan 5 alpha tan 3 alpha

If alpha_1, ,alpha_2,.... ,alpha_n are the roots of equation x^n+n a x-b=0, show that (alpha_1-alpha_2)(alpha_1-alpha_3).......(alpha_1-alpha_n)=n(alpha_1^ (n-1)+a)

Prove that, (1+ cos 2 alpha + sin 2 alpha)/(1-cos 2 alpha +sin 2 alpha)=cot alpha

If alpha is a cube root of unity , then find the value of |{:(alpha,alpha^3,alpha^5),(alpha^3,alpha^5,alpha),(alpha^5,alpha,alpha^3):}|

If the roots of equation x^3+a x^2+b=0a r ealpha_1,alpha_2 and alpha_3(a ,b!=0) , then find the equation whose roots are (alpha_1alpha_2+alpha_2alpha_3)/(alpha_1alpha_2alpha_3),(alpha_2alpha_3+alpha_3alpha_1)/(alpha_1alpha_2alpha_3),(alpha_1alpha_3+alpha_1alpha_2)/(alpha_1alpha_2alpha_3)

If 4nalpha=pi , then the numerical value of tanalpha, tan2alpha,tan3alpha.....tan(2n-1)alpha is equal to

Prove that, (sec 8 alpha -1)/(sec 4 alpha-1)= (tan 8 alpha)/(tan 2 alpha