Simplify 2+csc(40)^2-cot(40)^2

Problem

2+csc2(40)−cot2(40)

Solution

1. Identify the trigonometric identity relating the cosecant and cotangent functions.

2. Recall the Pythagorean identity for these functions:

csc2(θ)−cot2(θ)=1

3. Substitute the value of the identity into the expression, where θ=40

csc2(40)−cot2(40)=1

4. Add the remaining constant to the result of the identity:

2+1=3

Final Answer

2+csc2(40)−cot2(40)=3

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