Show that: `cos\ pi/n +cos\ (2pi)/n +…+cos\ (n-1)/n pi =0`

Show that if n gt 2 cos^2 (pi/n) + cos^2 ((3pi)/n)+ cos^2((5pi)/n)+ ... n terms =n/2

Show that cos(pi/65)cos((2pi)/65)cos((4pi)/65)cos((8pi)/65)cos((16pi)/65)cos((32pi)/65)=1/64

Show that cos(pi/15)cos((2pi)/15)cos((3pi)/15)cos((4pi)/15)cos((5pi)/15)cos((6pi)/15)cos((7pi)/15) = 1/2^7

Let n be a positive integer such that sin (pi/(2n))+cos (pi/(2n))= sqrt(n)/2 then (A) n=6 (B) n=1,2,3,….8 (C) n=5 (D) none of these

If theta = (pi)/(2 ^(n) +1) prove that 2 ^(n) cos theta cos 2 theta cos 2 ^(2) theta…. Cos 2 ^(n -1) theta =1

If 7theta=(2n+1)pi , where n=0,1,2,3,4,5,6 , then answer the following questions. The equations whose roots are cos. (pi)/(7), cos. (3pi)/(7), cos. (5pi)/(7) is

The area of the circle and the area of a regular polygon of n sides and the perimeter of polygon equal to that of the circle are in the ratio of tan(pi/n):pi/n (b) cos(pi/n):pi/n sinpi/n :pi/n (d) cot(pi/n):pi/n

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

If S=cos^2pi/2+cos^2(2pi)/n+....+cos^2((n-1)pi)/(n), then S equals

the sum of the radii of inscribed and circumscribed circle of an n sides regular polygon of side a is (A) a/2 cot (pi/(2n)) (B) acot(pi/(2n)) (C) a/4 cos, pi/(2n)) (D) a cot (pi/n)