If `cos A+s in B=m\ a n d\ s in 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 , prove that 2sin(A+B)=m^2+n^2-2.

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 3t a n At a n B=1, prove that 2cos(A+B)=cos(A-B)dot

If acostheta+bsintheta=m and asintheta-bcostheta=n , prove that a^2+b^2=m^2+n^2

If cos e ctheta-sintheta=m and sectheta-costheta=n , prove that (m^(2)n)^(2/3)+(m n^2)^(2/3)=1

If sin A + cos A = m and sin^3 A + cos^3A=n , then (1) m^3-3m + n = 0 (2) n^3-3n + 2m=0 (3) m^3-3m + 2n = 0 (4) m3 + 3m + 2n = 0

If acostheta+bsintheta=m and asintheta-bcostheta=n , Prove that a^2+b^2=m^2+n^2

If m = a sec A + b tan A and n = a tan A + b sec A, then prove that : m^(2) - n^(2) = a^(2) - b^(2)

If sin A+sin B=alpha\ a n d\ cos A+cos B=beta, then write the value of tan((A+B)/2)dot