If A + B + C + D = 2 π, prove that: cos ⁡...

Cierra Castillo

Cierra Castillo

Answered

2022-06-30

If A + B + C + D = 2 π, prove that: cos A + cos B + cos C + cos D = 4 cos A + B 2 cos A + C 2 cos B + C 2

Answer & Explanation

iskakanjulc

iskakanjulc

Expert

2022-07-01Added 18 answers

We will use 2 cos X cos Y = cos ( X + Y ) + cos ( X Y )
4 cos A + B 2 cos A + C 2 cos B + C 2 = 2 ( cos ( A + B + C 2 ) + cos B C 2 ) cos B + C 2 = 2 cos ( A + B + C 2 ) cos B + C 2 + 2 cos B C 2 cos B + C 2 = cos ( A + B + C ) + cos A + cos B + cos C = cos ( 2 π D ) + cos A + cos B + cos C = cos A + cos B + cos C + cos D

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