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The Second one, still easy!

Source: 1981 National High School Mathematics League, Problem 2

February 20, 2020

Problem Statement

Given two conditions: A: 1+sin⁡θ=a\sqrt{1+\sin\theta}=a B: sin⁡θ2+cos⁡θ2=a\sin\frac{\theta}{2}+\cos\frac{\theta}{2}=a Then, which one of the followings are true? (A)(\text{A})A is sufficient and necessary condition of B. (B)(\text{B})A is necessary but insufficient condition of B. (C)(\text{C})A is sufficient but unnecessary condition of B. (D)(\text{D})A is insufficient and unnecessary condition of B.
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