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Find sin θ+cos θ

Source: 1976 AHSME Problem 17

May 18, 2014
trigonometryAMC

Problem Statement

If θ\theta is an acute angle, and sin⁡2θ=a\sin 2\theta=a, then sin⁡θ+cos⁡θ\sin\theta+\cos\theta equals
<spanclass=′latex−bold′>(A)</span>a+1<spanclass=′latex−bold′>(B)</span>(2−1)a+1<spanclass=′latex−bold′>(C)</span>a+1−a2−a<span class='latex-bold'>(A) </span>\sqrt{a+1}\qquad<span class='latex-bold'>(B) </span>(\sqrt{2}-1)a+1\qquad<span class='latex-bold'>(C) </span>\sqrt{a+1}-\sqrt{a^2-a}\qquad
<spanclass=′latex−bold′>(D)</span>a+1+a2−a<spanclass=′latex−bold′>(E)</span>a+1+a2−a<span class='latex-bold'>(D) </span>\sqrt{a+1}+\sqrt{a^2-a}\qquad <span class='latex-bold'>(E) </span>\sqrt{a+1}+a^2-a
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