Question 694871
Show {{{ ln (abs(csc(theta) +1)) + ln (abs(csc(theta) -1)) = 2ln (abs(cot(theta))) }}}

Now {{{ ln (abs(csc(theta) +1)) + ln (abs(csc(theta) -1)) }}}

{{{ "" = ln (abs((csc(theta) + 1)(csc(theta) -1 ))) }}} (using {{{ log(A)+log(B)=log(AB) }}} )

{{{ "" = ln( abs( (csc(theta) + 1)(csc(theta) - 1 )) )) }}}
{{{ "" = ln( abs( csc^2(theta) -1 )) }}}
{{{ "" = ln( abs( cot^2(theta) )) }}} (using {{{ 1 + cot^2(theta) = csc^2(theta) }}})
{{{ "" = ln( abs( cot(theta) )^2 ) }}}
{{{ "" = 2ln( abs( cot(theta) ) ) }}}