[" If "n" is an integer,prove that,"],[" (i) "cos(n pi+theta)=(-1)^(n)cos theta]

If n is an integer,prove that cos(n pi+theta)=(-1)^(n)cos theta

If n is an integer then show that (1 + cos theta + i sin theta)^(n) + (1 + cos theta - i sin theta )^(n) = 2^(n+1) cos ^(n) ( theta//2) cos ((n theta)/2) .

If n is a positive integer,prove the following (1+cos theta+i sin theta)+(1+cos theta-i sin theta)^(n)=2^(n+1)cos^(n)((theta)/(2))cos((n theta)/(2))

If n is an integer and if sin theta=1, prove that theta=(4n+1)(pi)/(2)

If n is a positive integer prove that (1+i)^(2n)+(1-i)^(2n)=2^(n+1)cos((n pi)/(2))

If sin (pi cot theta)= cos (pi tan theta) and n is an integer, then prove that the value of cot 2 theta is of the form (1)/(4) +k .

Using De Moivre 's theorem prove that : ((1+cos theta +i sin theta)/(1+cos theta - i sin theta))^n= cos n theta + i sin n theta , where i = sqrt(-1)

If n is an integer and z=cos theta+i sin theta , then (z^(2 n)-1)/(z^(2 n)+1)=

If A = [(cos theta, sin theta),(-sin theta, cos theta)] then show that for all the positive integers n, A^(n) = [(cos n theta,sin n theta),(-sin n theta,cos n theta)] .

If A=[[cos theta,sin theta-sin theta,cos theta]] then prove that A^(n)=[[cos n theta,sin n theta-sin n theta,cos n theta]],n in N