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)`

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))=nalpha_(1)^(n-1)+nalpha

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

If alpha_1 , alpha_2, ......, alpha_n are in A.P, whose common difference is d , show that sin d [ sec alpha_1 sec alpha_2 + sec alpha_2 sec alpha_3 +.......+ sec alpha_(n - 1) sec alpha_n] = tan alpha_n - tan alpha_1

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 1,alpha_1,alpha_2, ,alpha_(n-1) are the n t h roots of unity, prove that (1-alpha_1)(1-alpha_2)(1-alpha_(n-1))=ndot Deduce that sin(pi/n)sin(2pi/n) sin((n-1)pi/n)=n/(2^(n-1))

IF the roots of the equation 3x^2+8x+2=0 are alpha,beta then (1/alpha+1/beta) =

show that (1-sin^2 alpha)(1-cos^2 alpha)(1+cot^2 alpha)(1+tan^2 alpha) = 1.

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