Use trigonometric identities to simplify the expression.1cot2(x)+tan(x)tan(π2−x)

Sure, let's simplify the expression step by step using trigonometric identities.

Given expression is: 1/cot^2(x) + tan(x)tan(π/2−x)

Step 1: Convert cot^2(x) to tan^2(x). We know that cot(x) = 1/tan(x), so cot^2(x) = 1/tan^2(x). Therefore, the expression becomes:

1/(1/tan^2(x)) + tan(x)tan(π/2−x)

Step 2: Simplify the first term. 1 divided by 1/tan^2(x) is just tan^2(x). So, the expression becomes:

tan^2(x) + tan(x)tan(π/2−x)

Step 3: Use the identity tan(π/2 - x) = cot(x) = 1/tan(x). So, the expression becomes:

tan^2(x) + tan(x) * 1/tan(x)

Step 4: Simplify the second term. tan(x) times 1/tan(x) is just 1. So, the expression becomes:

tan^2(x) + 1

This is the simplified form of the given expression.