The maximum value of `(cos alpha_1). (cos alpha_2)...........(cos alpha_n)`, under the restrictions `0 <=alpha_1,alpha_2..........,alpha_n<=pi/2 and (cot alpha_1) (cot alpha_2) ......... (cot a_n)=1` is

Prove that the maximum value of (cos alpha_(1)) (cos alpha_(2))...( cos alpha_(r)) uder the restrictions 0 le alpha_(r) le (pi)/(2) (r=1, 2,..., n) and (cot alpha_(1)) (cot alpha_(2))...( cot alpha_(r))=1 "is" (1)/(2^(n/2))

The maximum value of (cosalpha_(1))-(cos alpha_(2))...(cosalpha_(n)), under the restrictions 0lealpha_(1),alpha_(2)...,alpha_(n)le(pi)/(2) and (cotalpha_(1))-(cotalpha_(2))......(cotalpha_(n))=1 is

The maximum value of (cosalpha_(1))(cos alpha_(2))...(cosalpha_(n)), under the restrictions 0lealpha_(1),alpha_(2)...,alpha_(n)le(pi)/(2) and (cotalpha_(1))(cotalpha_(2))......(cotalpha_(n))=1 is

The maximum value of (cosalpha_(1))(cos alpha_(2))...(cosalpha_(n)), under the restrictions 0lealpha_(1),alpha_(2)...,alpha_(n)le(pi)/(2) and (cotalpha_(1))(cotalpha_(2))......(cotalpha_(n))=1 is

The maximum value of determinant |{:(cos(alpha+beta),sin alpha,-cos alpha),(-sin(alpha+beta),cos alpha, sin alpha),(cos 2beta,sin beta, cos beta):}| is ___________

If alpha=(pi)/(7) then find the value of ((1)/(cos alpha)+(2cos alpha)/(cos2 alpha))

If alpha=(pi)/(7), then find the value of ((1)/(cos alpha)+(2cos alpha)/(cos2 alpha))

Sum the series : (1+cos alpha) +(1+ cos2alpha) +(1+ cos3alpha) +..... to n terms.

If alpha_(1),alpha_(2)………., alpha_(n) are real numbers show that (cos alpha_(1)+cos alpha_(2)+…..+cos alpha_(n))^(2)+(sin alpha_(1)+……+sin alpha_(n))^(2) le n^(2)

If n=1,2,3,......, then cos alpha cos2 alpha cos4 alpha.........cos2^(n-1)alpha is equal to