If `m cosalpha-nsinalpha=p` then prove that `msinalpha+ncosalpha=+-sqrt(m^2+n^2-p^2)`

If tantheta=ntanalpha and sintheta=msinalpha then prove that cos^(2)theta=(m^(2)-1)/(n^(2)-1),n!=+-1.

If (cosalpha)/(cosbeta)=m and (cosalpha)/(sinbeta)=n then prove that (m^(2)+n^(2))cos^(2)beta=n^(2) .

If cosalpha/cosbeta=m and cosalpha/sinbeta=n then Show that (m^2+n^2) cos^2beta=n^2 .

If A.M. and G.M. between two numbers is in the ratio m : n then prove that the numbers are in the ratio (m+sqrt(m^2-n^2)):(m-sqrt(m^2-n^2))dot

If A.M.and G.M.between two numbers is in the ratio m:n then prove that the numbers are in the ratio (m+sqrt(m^(2)-n^(2))):(m-sqrt(m^(2)-n^(2)))

If A.M. and G.M. between two numbers is in the ratio m : n then prove that the numbers are in the ratio (m+sqrt(m^2-n^2)):(m-sqrt(m^2-n^2))dot

If A.M. and G.M. between two numbers is in the ratio m : n then prove that the numbers are in the ratio (m+sqrt(m^2-n^2)):(m-sqrt(m^2-n^2))dot

If A.M. and G.M. between two numbers is in the ratio m : n then prove that the numbers are in the ratio (m+sqrt(m^2-n^2)):(m-sqrt(m^2-n^2))

If the ratio of A.M. and G.M. of two positive numbers a and b is m : n, then prove that : a:b=(m+sqrt(m^(2)-n^(2))):(m-sqrt(m^(2)-n^(2)))

If A.M. and G.M. between two numbers is in the ratio m : n then prove that the numbers are in the ratio (m+sqrt(m^2-n^2)):sqrt((m-m^2-n^2))dot