Problem:
If sin2xsin3x=cos2xcos3x, then one value for x is
Answer Choices:
A. 18∘
B. 30∘
C. 36∘
D. 45∘
E. 60∘
Solution:
The following statements are equivalent:
sin2xsin3x=cos2xcos3xcos2xcos3x−sin2xsin3x=0cos(2x+3x)=0,5x=90∘+180∘k,k=0,±1,±2,…x=18∘+36∘k,k=0,±1,±2,…
The only correct value listed among the answers is 18∘.
OR
By inspection of the original equation, it is sufficient that sin2x=cos3x and sin3x=cos2x, which are both true if 2x and 3x are complementary. Thus 2x+3x=90∘, i.e., x=18∘, is a correct value.