If (1+\cos A)(1+\cos B)(1+\cos C)=(1-\cos A)(1-\cos B)(1-\cos C) then prove that

Ezequiel Olson

Ezequiel Olson

Answered question

2022-04-22

If (1+cosA)(1+cosB)(1+cosC)=(1cosA)(1cosB)(1cosC)
then prove that each side
=±sinAsinBsinC

Answer & Explanation

retopire07c

retopire07c

Beginner2022-04-23Added 11 answers

Squaring both sides is equivalent to do the following
(1+cosA)(1+cosB)(1+cosC)(1cosA)(1cosB)(1cosC)=(1cosA)(1cosB)(1cosC)(1+cosA)(1+cosB)(1+cosC)
and using that 1cos2A=sin2A we get
sin2Asin2Bsin2C=sin2Asin2Bsin2C
hence the result.

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