Simplify cot2q + 1. a. csc2 q c. cot2 q b. 0 d. cos2 q

We know that cotangent is the reciprocal of tangent equal to sinθ/cosθ, that is, cotθ is equal to cosθ/sinθ, cot²q + 1 =  (cos²q/sin²q) + 1 To make the denominators the same for the terms on the right hand side of our equation, we can convert the term 1 to an equivalent fraction sin²θ/sin²θ:cot²q + 1 = cos²q/sin²q + sin²q/sin²qcot²q + 1 = (cos²q + sin²q)/sin²q Using the equation cos²θ + sin²θ = 1 derived from the Pythagorean theorem which relates sine with cosine, we now havecot²q + 1 = 1/sin²qand since cscθ is equal to 1/sinθ based from Reciprocal identities that define sine in terms of cosecant, we can also write our expression intocot²q + 1 = csc²qTherefore, the answer is a. csc²q