Find the Domain sec(x)cot(x)=csc(x)

Problem

sec(x)*cot(x)=csc(x)

Solution

1. Identify the individual functions in the equation. The equation involves sec(x) cot(x) and csc(x)

2. Determine the constraints for sec(x) Since sec(x)=1/cos(x) the function is undefined when cos(x)=0 This occurs at x=π/2+n*π for any integer n

3. Determine the constraints for cot(x) Since cot(x)=cos(x)/sin(x) the function is undefined when sin(x)=0 This occurs at x=n*π for any integer n

4. Determine the constraints for csc(x) Since csc(x)=1/sin(x) the function is undefined when sin(x)=0 This occurs at x=n*π for any integer n

5. Combine all restrictions. The domain must exclude values where sin(x)=0 or cos(x)=0 These combined points are x=(n*π)/2 for any integer n

Final Answer

Domain:{x|x≠(n*π)/2,n∈ℤ}

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