`(1+cos theta + sin theta)/(1-cos theta + sin theta)`

Prove that ((1+cos theta+i sin theta)/(1+cos theta-i sin theta))^(n)=cos n theta+i sin n theta

Prove each of the following identities : (cos theta) /((1- tan theta)) - (sin^(2) theta)/((cos theta - sin theta)) = (cos theta + sin theta)

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 theta=(pi)/(6) then the 10^(th) term of the series : 1+(cos theta+i sin theta)^(1)+(cos theta+i sin theta)^(2)+

if theta=(pi)/(6) then the 10 th term of the series 1+(cos theta+i sin theta)^(1)+(cos theta+i sin theta)^(2)+

If theta=(pi)/(6) then find the 10 th term of the series 1+(cos theta+i sin theta)^(1)+(cos theta+i sin theta)^(2)+...

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))

The value of (1+cos theta+i sin theta)^(n)+(1+cos theta-i sin theta)^n=

The value of (1+cos theta+i sin theta)^(n)+(1+cos theta-i sin theta)^(n)=

cos theta/(1+sin theta)=(1-sin theta)/cos theta