SOLUTION: if cot(tan(x)) =tan(cot(x)), then sin(2x) =.....

Question 1191899: if cot(tan(x)) =tan(cot(x)), then sin(2x) =.....
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!





Cross-multiply:



Get 0 on the right side:



Use the identity 



So tan(x)+cot(x) must equal to any odd integer multiple of 

The general odd integer is 2n+1 for any integer n









Take reciprocals of both sides:



Multiply numerator and denominator on the right side by 2



Multiply both sides by 2 and reverse the factors on the left side
to make the left side look like the right side of the 
identity 



, where n is any integer.

Edwin

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