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Chapter 8: Q. 58 (page 529)

Mollweide鈥檚 Formula For any triangle, Mollweide鈥檚 Formula (named after Karl Mollweide, 1774鈥�1825) states that a+bc=cos12A-Bsin12C

Derive it.

[Hint: Use the Law of Sines and then a Sum-to-Product Formula. Notice that this formula involves all six parts of a triangle. As a result, it is sometimes used to check the solution of a triangle.]

Short Answer

Expert verified

This is proved thata+bc=cos12A-Bsin12C

Step by step solution

01

Step 1. Given Information

Use sinAa=sinBb=sinCcLawofSines

Sum of angles in a triangle A+B+C=180鈭�

Sum to product formula sinA+sinB=2sinA+B2cosA-B2

Co-function identity sin90鈭�-胃=cos胃

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