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

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

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

If sin A = sin B and cos A = cos B , then show that A = 2n pi + B, n in Z

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

If (cos x)/(cos y) = n , (sin x)/(sin y) = m , then what is (m^2 - n^2) sin^2 y equal to ?

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 (cos alpha)/(cos beta)=m and (cos alpha)/(sin beta)=n show that (m^(2)+n^(2))cos^(2)beta=n^(2)

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