Problem: If tanx=a2−b22ab where a>b>0 and 0∘<x<90∘, then sinx is equal to
Answer Choices:
A. ba
B. ab
C. 2aa2−b2
D. 2aba2−b2
E. a2+b22ab
Solution:
Angle x may be taken as the acute angle opposite the side af langth 2ab in a right triangle (See figure) whose other leg then hat length ( a2−b2 ). The hypothenuse is then the equare root of (2ab)2+(a2−b2)2=a4+2a2b2+b4 or a2+b2. Hence sin x=2ab/(a2+b2) by the defintion of sine.
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