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Trigonometric functions

Source: 1981 National High School Mathematics League, Problem 3

February 20, 2020
function

Problem Statement

Let α\alpha be a real number and α≠kπ2,k∈Z\alpha\neq\frac{k\pi}{2} , k\in\mathbb{Z}, T=sin⁡α+tan⁡αcos⁡α+cot⁡αT=\frac{\sin\alpha+\tan\alpha}{\cos\alpha+\cot\alpha}. (A)\text{(A)}TT is negative. (B)\text{(B)}TT is nonnegative. (C)\text{(C)}TT is positive. (D)\text{(D)}TT can be either positive or negative.
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