Im confused with setting up the criterion for a goniometric equation like 2cot²x-2sec²x=1 . I know how to solve it, we covert all to tanx with formulas "cot²x= 1/tan²x" & "1+tan²x=sec²x".Then we get [2/tan²x]-2(1+tan²x)=1 .But now we need to set up the criterion. I dont know though whether what im doing is correct.
I like to set up the criterion as follows: now that we converted to tanx we have to mention that FOR tanx: x≠(π/2)+kπ . However there was no tanx at first in the original equation: 2cot²x-2sec²x=1 . Therefore we have to fill in (π/2)+kπ into the original equation to see whether its a solution of the original equation.We know for a fact that (π/2)+kπ cant be a solution to [2/tan²x]-2(1+tan²x)=1, but maybe it can be the solution to the original equation. This is why we have to enter the value of (π/2)+kπ into 2cot²x-2sec²x=1 to see whether it is a solution of the equation itself. Can someone please tell me whether my reasoning is correct here?
Also I forgot to mention that tanx≠0 so wed have to check for x=0 also in the original equation to see whether its a solution to the original equation.
Thank you!!
