" cot "theta(1+sin theta)=4m" and "cot theta(1-sin theta)=4n," prove that "(m^(2)-n^(2))^(2)=mn

If cot theta(1+sin theta)=4man d cot theta(1-sin theta)=4n prove that (m^(2)-n^(2))^(2)=mn

If (tan theta + sin theta) =m and (tan theta - sin theta) = n , prove that (m^(2)-n^(2))^(2)=16mn.

If " cosec"theta-sin theta=m and sec theta-cos theta=n , then prove that (m^(2)n)^((2)/(3))+(mn^(2))^((2)/(3))=1.

If cos theta-sin theta=m and cos theta+sin theta=n then prove that (m^2-n^2)/(m^2+n^2)=-2sin theta cos theta

If cos ec theta-sin theta=m and sec theta-cos theta=n prove that (m^(2)n)^((2)/(3))+(mn^(2))^((2)/(3))=1

If cot theta + cos theta = m and cot theta - cos theta = n then prove that: m^(2) - n^(2) = 4sqrt(mn)

If tan theta+sin theta=m and tan theta-sin theta=n then prove m^(2)-n^(2)=4sqrt(mn)

If a cos theta+b sin theta=m and a sin theta-b cos theta=n, prove that a^(2)+b^(2)=m^(2)+n^(2)

If cos ec theta+cot theta=m and cos ec theta-cot theta=n, prove that mn=1

If a cos theta+b sin theta=m and a sin theta-b cos theta=n, Prove that a^(2)+b^(2)=m^(2)+n^(2)