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Grade 11Algebra

  1. Let x, y, z be real numbers such that x^2. Prove that (1+x)(1+y)(1+z)
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Profile image of abuzar
10 Years agoGrade 11
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1 Answer

Profile image of mycroft holmes
10 Years ago
Using the standard substitution, x = cos A, y = cos B, z = cos C, where A,B,C are angles of a triangle, we have to prove that
 
(1+cos A)(1+ cos B)(1+cos C)
 
We have (1+cos A)(1+cos B) =0 which is true)
 
Similarly (1+cos A cos B)(1+cos C)
 
Thus we have (1+cos A)(1+ cos B)(1+cos C)