Question

Verify the identity algebraically. Use the table feature of a graphing utility to check your result numerically. (Simplify at each step.)

Answer 1

The identity; 8/tan(x) + 8/cot(x) = 8·tan(x) + 8·cot(x) is correct using the definition of the tangent and cotangent of an angle

Please find attached the graphs of the expressions 8/tan(x) + 8/cot(x) and 8·tan(x) + 8·cot(x) showing that the functions are superposed, indicating that the identity is correct

The steps used to verify the identity are presented as follows;

The identity can be verified as follows;

8/tan(x) = 8·cot(x)

8/cot(x) = 8·tan(x), therefore;

8/tan(x) + 8/cot(x) = 8·cot(x) + 8·tan(x)

8·cot(x) + 8·tan(x) = 8·tan(x) + 8·cot(x)

Therefore; 8/tan(x) + 8/cot(x) = 8·tan(x) + 8·cot(x)

8/tan(x) + 8/cot(x) = (8·cot(x) + 8·tan(x))/(tan(x)×cot(x))

(tan(x)×cot(x)) = 1

(8·cot(x) + 8·tan(x))/(tan(x)×cot(x)) = (8·cot(x) + 8·tan(x))/1

(8·cot(x) + 8·tan(x))/(tan(x)×cot(x)) = (8·cot(x) + 8·tan(x))/1

8/tan(x) + 8/cot(x) = 8·cot(x) + 8·tan(x)

8/tan(x) + 8/cot(x) =8·tan(x) + 8·cot(x)

The values of the above equation can be