Question 1180758
see my worksheet below.


<img src = "http://theo.x10hosting.com/2021/052101.jpg">


i used x instead of theta.
no change in the formulas except a change of variable name.


step 1 shows the original equation.


step 2 changes cot(x) to equivalent form of 1/tan(x). and changes sec(x) to equivalent form of 1/co(x).


step 3 converts 1/(1/tan(x)) to equivalent form of tan(x) and converts 1/(1/cos(x)) to equivalent form of cos(x).


note that 1/tan(x) * 1/cos(x) is equivalent to 1 / (tan(x)*cos(x)) and that 1 / (1 / (tan(x)*cos(x))) = tan(x) * cos(x).


step 4 converts tan(x) to equivalent form of sin(x) / cos(x).


step 5 cancels cos(x) in numberator and denominator, leaving sin(x) = sin(x) which is true.


the original equation is confirmed to be true.