Question 1106777
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{{{(cot(x))^2 / (csc(x) + 1) = (1 - sin x) / sin x}}}<br>
Work on the left hand side to make it look like the right hand side.<br>
{{{((cos(x))^2/(sin(x))^2) / ((1/sin(x))+1)}}}   Change everything to sin(x) and cos(x):<br>
{{{((cos(x))^2/(sin(x))^2) / ((1+sin(x))/sin(x))}}}  get common denominator in the denominator<br>
{{{((cos(x))^2/(sin(x))^2) * (sin(x)/(1+sin(x)))}}}   divide fractions: "flip and multiply"<br>
{{{(cos(x))^2/((sin(x))*(1+sinx))}}}  simplify<br>
{{{((1-sin(x))^2)/((sin(x))*(1+sinx))}}}   use Pythgorean identity to get everything in terms of sin(x)<br>
{{{((1-sin(x))(1+sinx))/((sin(x))*(1+sinx))}}}   factor<br>
{{{(1-sin(x))/sin(x)}}}   cancel common factor<br>
DONE!  The left hand side is now the same as the right hand side.