Question 187494
I'm assuming that you want to prove that {{{cot(x)*cos(x)=cot(x)-cos(x)}}} is an identity right?



There's a problem here, the equation:



{{{cot(x)*cos(x)=cot(x)-cos(x)}}}



is NOT an identity (graph the two sides if you aren't sure)


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For example, let {{{x=1}}}



{{{cot(x)*cos(x)=cot(x)-cos(x)}}} Start with the given equation.



{{{cot(1)*cos(1)=cot(1)-cos(1)}}} Plug in {{{x=1}}}



{{{(0.642)*(0.540)=0.642-0.540}}} Evaluate the given trig functions (note: I'm working in radian mode).



{{{0.34668=0.102}}} Simplify. Clearly the two sides are NOT equal.



Since {{{0.34668<>0.102}}}, this means that the equation is NOT true for ALL values of "x". So the equation is NOT an identity.




So either there's a typo or you were supposed to disprove it being an identity. My guess would be that there's a typo in there somewhere.



Note: if you change the "cot" to "csc" and "cos" to "sin" on the right, you'll get  {{{cot(x)*cos(x)=csc(x)-sin(x)}}} which is an identity