Question 140791
I can show you how to add the fractions, but since there is no equal sign anywhere, there is no "identity"


You add the fractions just like you would add any other fractions.  You find a common denominator, convert the numerators, and then sum the numerators.


{{{(sin(x)/(cos(x)+1))((cos(x)+1)/sin(x))}}}


The two denominators have no factors in common, so the lowest common denominator is simply the product of the denominators, exactly like adding {{{1/5+1/7}}} where the LCD is just {{{5*7=35}}}


So your LCD is {{{sin(x)(cos(x)+1)}}} and your sum becomes:


{{{(sin^2(x)+(cos(x)+1)^2)/(sin(x)(cos(x)+1))}}}


{{{(sin^2(x) + cos^2(x)+2cos(x)+1)/(sin(x)(cos(x)+1))}}}


But we know that {{{sin^2(x)+cos^2(x)=1}}} so:


{{{(1+2cos(x)+1)/(sin(x)(cos(x)+1))}}}


{{{(2cos(x)+2)/(sin(x)(cos(x)+1))}}}


{{{cartoon((2(cos(x)+1))/(sin(x)(cos(x)+1)),(2*cross((cos(x)+1)))/(sin(x)cross((cos(x)+1))))}}}



{{{2/sin(x)}}}


{{{2csc(x)}}}