The Problem:
Evaluate the following algebraic expression without using a calculator, slide rule, or computer, and without evaluating any trigonometric functions:
sin(13°) * sin(77°) / sin(154°)
The Solution:
sin(13°)sin(77°)/sin(154°)
= sin(13°)cos(13°)/sin(154°) (because sin(x)=cos( 90°-x))
= sin(13°)cos(13°)/sin( 26°) (because sin(x)=sin(180°-x))
= sin(13°)cos(13°)/sin(2*13°) (because 26=2*13)
= sin(13°)cos(13°)/2sin(13°)cos(13°) (because sin(2x)=2sin(x)cos(x))
= 1/2 (because everything else cancels-out!)
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