" (xi) "(2)/(1+cos theta+i sin theta)

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

If (2+i)r^(-1)={4i+(1+i)^(2)}(cos theta+i sin theta) then value of r is

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) .

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

Simplify ((1 + cos 2 theta + i sin 2 theta)/(1 + cos 2 theta - i sin 2 theta))^(30)

The modulus of the complex number ((1-isqrt3)(cos theta+isin theta))/(2(1-i) (cos theta-i sin theta)) is

If ((1 + cos theta + i sin theta ) /(i+ sin theta + i cos theta ))= cos ntheta + i sin n theta then n is equal to :