[" If "(sin theta_(1)+i cos theta_(1))(cos theta_(2)+i sin theta_(2))....],[(sin theta_(n)+i cos theta_(n))=a+ib,a^(2)+b^(2)=]

If Cos theta_(1) + Cos theta_(2) + Cos theta_(3) = 3 then Sin theta_(1) + Sin theta_(2) + Sin theta_(3) =

If sum_(i=1)^(n)sin theta_(i)=n then cos theta_(1) + cos theta_(2) + ...+cos theta_(n)=

If sin theta_(1)+sin theta_(2)+sin theta_(3)=3 then cos theta_(1)+cos theta_(2)+cos theta_(3)=

If Sin theta_(1) + Sin theta_(2) + Sin theta_(3) = 3 then Cos theta_(1) + Cos theta_(2) + Cos theta_(3) =

2(cos theta+cos2 theta)+(1+2cos theta)sin2 theta=2sin theta

(cos theta + i sin theta) ^ (n) = cos n theta + i sin n theta

If (cos theta_(1))/(cos theta_(2))+(sin theta_(1))/(sin theta_(2))=(cos theta_(0))/(cos theta_(2))+(sin theta_(0))/(sin theta_(2))=1 , where theta_(1) and theta_(0) do not differ by can even multiple of pi , prove that (cos theta_(1)*cos theta_(0))/(cos^( 2)theta_(2))+(sin theta_(1)*sin theta_(0))/(sin^(2) theta_(2))=-1

If (cos theta_(1))/(cos theta_(2))+(sin theta_(1))/(sin theta_(2))=(cos theta_(0))/(cos theta_(2))+(sin theta_(0))/(sin theta_(2))=1 , where theta_(1) and theta_(0) do not differ by can even multiple of pi , prove that (cos theta_(1)*cos theta_(0))/(cos^( 2)theta_(2))+(sin theta_(1)*sin theta_(0))/(sin^(2) theta_(2))=-1

If (cos theta_(1))/(cos theta_(2))+(sin theta_(1))/(sin theta_(2))=(cos theta_(0))/(cos theta_(2))+(sin theta_(0))/(sin theta_(2))=1 , where theta_(1) and theta_(0) do not differ by can even multiple of pi , prove that (cos theta_(1)*cos theta_(0))/(cos^( 2)theta_(2))+(sin theta_(1)*sin theta_(0))/(sin^(2) theta_(2))=-1