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If A+B+C=180 degrees then what is the value of cos2A + cos 2 B + cos 2 C

If A+B+C=180 degrees then what is the value of cos2A + cos 2 B + cos 2 C

Grade:8

1 Answers

Avik Kundu
20 Points
6 years ago
A+B+C=\prod
LHS = cos 2A ± cos 2B + cos 2C
= 2 cos (A ± B) cos (A — B) ± cos 2C
= 2 cos (ir — C) cos (A — B) ± 2 cos2 C — 1
= —2 cosc. cos (A — B) ± 2 cost C — 1
= —1 + 2 cosC(cosC — cos(A — B))
= —1 + 2 cosC(cos(ir — (A + B) — cos(A — B))
== —1 + 2 cosC(— cos(A + B) — cos(A — B))
= —1 — 4 cosAcosBcosC

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