Question 1182315
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After replacing your "0" with "theta", the equation as you show it is this:<br>
{{{sin(theta)/1-cos(theta)-sin(theta)/1+cos(theta) = 2/tan(theta)}}}<br>
That equation is not true....<br>
If your study of math has reached the point where you are learning proving trig identities, then you should know that proper use of parentheses is important....!<br>
Let's look at the left-hand side of the inequality you INTENDED to show and see if we can show it is equivalent to the right-hand side.<br>
{{{sin(theta)/(1-cos(theta)) - sin(theta)/(1+cos(theta))}}}<br>
Combine fractions with the common denominator, {{{(1-cos(theta))(1+cos(theta))=1-cos^2(theta)=sin^2(theta)}}}<br>
{{{(sin(theta)(1+cos(theta))-sin(theta)(1-cos(theta)))/sin^2(theta)}}}<br>
{{{(sin(theta)+sin(theta)cos(theta)-sin(theta)+sin(theta)cos(theta))/sin^2(theta)}}}<br>
{{{(2sin(theta)cos(theta))/sin^2(theta)}}}<br>
{{{2cos(theta)/sin(theta)}}}<br>
{{{2cot(theta)}}}<br>
{{{2/tan(theta)}}}<br>
The proof is complete.<br>