Problem: If 0 is an acute angle and sin2θ=a, then sinθ+cosθ equals
Answer Choices:
A. a+1
B. (2−1)a+1
C. a+1−a2−a
D. a+1+a2−a
E. a+1+a2−a
Solution:
By virtue of the trigonometric identities,
(sinθ+cosθ)2=sin2θ+cos2θ+2sinθcosθ=1+sin2θ=1+a
Since θ is acute, sinθ+cosθ>0 and sinθ+cosθ=1+a.