If `cos A+sin B=m` and `sin A+cos B=n ,` prove that `2sin(A+B)=m^2+n^2-2.`

If cos A+sin B=m and Sin A+cos B=n ,then prove that 2sin (A+B)=m^2+n^2-2 .

lfcos A+s in B=m and s in A+cos B=n prove that 2sin(A+B)=m^(2)+n^(2)-2

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

If x cos A + y sin A = m and x sin A - y cos A = n, then prove that : x^(2) + y^(2) = m^(2) + n^(2)

If tan A=n tan B and sin A=m sin B, prove that cos^(2)A=(m^(2)-1)/(n^(2)-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)

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

If tan A = n tan B and sin A = m sin B, prove that : cos^(2) A = (m^(2) - 1)/(n^(2) - 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)

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