Answer to Question #100466 in Geometry for biruk

Question

show that cos2a+cos2B+cos2r=1

Answer 1

If A, B, R are angles with respect to the coordinate axes then we will use that cos²A+cos²B+ cos²R = 1.

So we know that 1+cos(2A) = 2cos²A, we get 2cos²A+2cos²B+ 2cos²R = 2;

1+cos(2A) +1+cos(2B)+1+cos(2R) = 2;

cos(2A)+cos(2B)+cos(2R) +1 = 0.