document.write( "Question 938710: cot(theta) = (2n^2+2mn)/(m^2+2mn) , then prove that cosec(theta)=(m^2+2mn+2n^2)/(m^2+2mn) \n" ); document.write( "
Algebra.Com's Answer #571895 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
cot(theta) = (2n^2+2mn)/(m^2+2mn) ,
\n" ); document.write( "then prove that
\n" ); document.write( "cosec(theta)=(m^2+2mn+2n^2)/(m^2+2mn)
\n" ); document.write( "------
\n" ); document.write( "Since cot = y/x, y = 2n^2+2mn and x = m^2+2mn
\n" ); document.write( "-----
\n" ); document.write( "Similarly, csc = r/x
\n" ); document.write( "------
\n" ); document.write( "r = sqrt[x^2+y^2] = sqrt[(m^2+2mn)^2 + (2n^2+2mn)^2]
\n" ); document.write( "---
\n" ); document.write( "= sqrt[(m(m+2n))^2 +(2n(n+m))^2]
\n" ); document.write( "---
\n" ); document.write( "= sqrt[(m^2(m^2+4mn+4n^2)) + (4n^2(n^2+2mn+m^2))]
\n" ); document.write( "====
\n" ); document.write( "= sqrt[m^4 + 4m^3n + 4m^2n^2 + 4n^4 + 8mn^3 + 4n^2m^2]
\n" ); document.write( "----
\n" ); document.write( "= sqrt[m^4 + 4m^3n + 8m^2n^2 + 8mn^3 + 4n^4]
\n" ); document.write( "---
\n" ); document.write( "= sqrt[m^2+2mn+2n^2]^2
\n" ); document.write( "----
\n" ); document.write( "= m^2+2mn+2n^2
\n" ); document.write( "=============
\n" ); document.write( "Therefore csc(theta) = r/x = (m^2+2mn+2n^2)/(m^2+2mn)
\n" ); document.write( "============
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( "-----------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );