\hspace{-16}$Is There is any Relation exists b/w the angle $\bf{M\;\;,N}$ and $\bf{P}$ Such \\\\ that $\bf{\cos^2(M)+\cos^2(N)+\cos^2(P)+2.\cos(M).\cos(N).\cos(P)=1}$
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2 Answers
36ya...
M + N + P = pi
proof...
M + N + P = pi
=> M + N = pi - P
=> cos (M + N) = - cos P
=> cosM.cosN - sinM.sinN = - cosP
=> cosM.cosN + cosP = sinM.sinN
=> cos2M.cos2N + cos2P + 2cosM.cosN.cosP = (1 - cos2M)(1 - cos2N)
=> cos2M.cos2N + cos2P + 2cosM.cosN.cosP = 1 - cos2N - cos2M + cos2M.cos2N
=> cos2 + cos2M + cos2N + 2cosM.cosN.cosP = 0
thus, M + N + P = pi.........!!
