Problem:
cos10∘+cos20∘sin10∘+sin20∘ equals
Answer Choices:
A. tan10∘+tan20∘
B. tan30∘
C. 21(tan10∘+tan20∘)
D. tan15∘
E. 41tan60∘
Solution:
Two trigonometric identities for expressing sums as products are:
sinx+siny=2sin2x+ycos2x−ycosx+cosy=2cos2x+ycos2x−y.
Thus cos10∘+cos20∘sin10∘+sin20∘=cos15∘sin15∘=tan15∘.