To solve the problem, we need to use the identities of trigonometric functions and their inverses.

Step 1: Rewrite the expression using the identities of cot and tan.

cot(tan^(-1)(2x) + cot^(-1)(2x)) = cot(arctan(2x) + arccot(2x))

Step 2: Use the property that arctan(x) + arccot(x) = π/2.

cot(π/2) = 0

So, cot(tan^(-1)(2x) + cot^(-1)(2x)) = 0 for all real x.

Question

To solve the problem, we need to use the identities of trigonometric functions and their inverses.

Step 1: Rewrite the expression using the identities of cot and tan.

cot(tan^(-1)(2x) + cot^(-1)(2x)) = cot(arctan(2x) + arccot(2x))

Step 2: Use the property that arctan(x) + arccot(x) = π/2.

cot(π/2) = 0

So, cot(tan^(-1)(2x) + cot^(-1)(2x)) = 0 for all real x.

Knowee AI · Accepted Answer

To solve the problem, we need to use the identities of trigonometric functions and their inverses.

Step 1: Rewrite the expression using the identities of cot and tan.

cot(tan^(-1)(2x) + cot^(-1)(2x)) = cot(arctan(2x) + arccot(2x))

Step 2: Use the property that arctan(x) + arccot(x) = π/2.

cot(π/2) = 0

So, cot(tan^(-1)(2x) + cot^(-1)(2x)) = 0 for all real x.

Evaluate cot(tan−1(2𝑥) + cot−1(2𝑥)).