[" The minimum value of "(1+(1)/(sin^(n)alpha))(1+(1)/(cos^(n)alpha))" is "],[1.01],[" 2."quad 2],[" 3."quad (1+2^(n/2))^(2)],[" 4."quad " none of these "]

if cos^(2)alpha-sin alpha=(1)/(n) then alpha

( sin(n+1) alpha - sin (n-1)alpha )/( cos (n+1) alpha + 2 cos n alpha + cos (n-1) alpha )=

cos (n + 1) alpha cos (n-1) alpha + sin (n + 1) alpha sin (n-1) alpha =

The maximum value of ( cos alpha_1) ( cos alpha_2) … ( cos alpha_n) under the restrictions 0 le alpha_1, alpha_2 ....... alpha_n le (pi)/(2) and cot alpha_1. cot alpha_2 ……cot alpha_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))

(1+sin alpha)/(1+cos alpha)*(1+sec alpha)/(1+cos ec alpha)=tan alpha

cos(n+1) alpha * cos(n-1)alpha + sin (n+1)alpha * sin (n-1) alpha =