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.`

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

If sin x+cos x=m and sec x+cos ecx=n prove that n(m^(2)-1)=2m

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 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 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

Prove that sin(A+B)sin(A-B)=cos^2B-cos^2A

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