Prove that `(cos (2pi r +- (pi)/4))/(sin{q pi + (-1)^q cdot (pi)/4}) = 1` where p and q are integers.

Prove that, cos(pi/5)-cos((2pi)/5)=1/2

Prove that 3 sin ""pi/6 sec ""pi/3 -4 sin ""(5pi)/(6) cot"" (pi)/(4) =1

Prove that cos ((pi)/(4) + x) + cos ((pi)/(4) -x) = sqrt2 cos x

If n is an integer, prove that, (iii) sin{n pi + (-1)^(n) cdot (pi)/6} = 1/2 .

Prove that sin (pi/14)sin((3pi)/14)sin((5pi)/14)=1/8

Prove that, 16 "cos" (2pi)/15 "cos" (4pi)/15 "cos" (8pi)/15 "cos" (16pi)/15 =1

Prove that, cos^(2) (pi/4) + sin^(2) (3pi/4) + sin^(2) (5pi/4) + sin^(2)(7pi/4) = 2 .

Prove that cos((2pi)/7)+cos((4pi)/7)+cos((6pi)/7)=-1/2

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

(i) If sin(pi/2costheta) = cos(pi/2 sin theta) , show that, +- cos(theta + pi/4) =(4n+1)/sqrt(2) where n= any integer. (ii) If tan(pi cos theta) = cot(pi sin theta) , prove that, cos(theta - pi/4) = (2n+1)/(2sqrt(2)), n=0, -1,1,-2,2 ,............