`2^(n-1)(cos theta-cos(pi/n))(cos theta-cos((2pi)/n))...(cos theta-cos((n-1)/n) pi)`

For a positive integer n, let f_(n)(theta)=(2cos theta+1)(2cos theta-1)(2cos2 theta-1)(2cos(2^(2))theta-1)...(2cos(2^(n-1))theta-1) Which one of the following hold(s) good?

Prove that sum_(r=1)^(n)((1)/(cos theta+cos(2r+1)theta))=(sin n theta)/(2sin theta*cos theta*cos(n+1)theta),(wherenin N)

If theta = pi/(2^(n) + 1), "show that",2^(n) cos theta cos 2 theta cos2^(2) theta cos2^(3) theta.... cos2^(n-1) theta = 1.

Let f_(n)(theta)=(cos((theta)/(2))+cos2 theta+cos((7 theta)/(2))+...+cos(3n-2)((theta)/(2)))/(sin((theta)/(2))+sin2 theta+sin((7 theta)/(2))+...+sin(3n-2)((theta)/(2))) then (a)f_(3)((3 pi)/(16))=sqrt(2)-1(b)f_(5)((pi)/(28))=sqrt(2)+1(c)f_(7)((pi)/(60))=(2+sqrt(3))(d) none of these

If theta =(pi)/(2 ^(n) +1), then cos theta cos 2 theta cos 2^(2) theta …cos 2 ^(n-1)theta is equal to

If theta =(pi)/(2 ^(n) +1), then cos theta cos 2 theta cos 2^(2) theta …cos 2 ^(n-1)theta is equal to ................... A) (1)/(2 ^(n)) B) cos theta C) 2 D) 2^(n)

cos theta+cos2 theta+cos3 theta+......+cos(n-1)theta+cos n theta=

If (cos x)/(cos theta)+(sin x)/(sin theta)=(cos y)/(cos theta)+(sin y)/(sin theta)=1 where x-y is not a multiple of 2 pi, then the value of (cos x*cos y)/(cos^(2)theta)+(sin x*sin y)/(sin^(2)theta)=......[theta!=n pi,(2n+1)(pi)/(2),n in z]

If theta_(1),theta_(2),theta_(3)....,theta_(n) are in A.P. then (sin theta_(1)+sin theta_(2)+...+sin theta_(n))/(cos theta_(1)+cos theta_(2)+...+cos theta_(n))=