Relation b/w M and N and P

BITSAT 2015 Discussion Forum › Trignometry questions › Relation b/w M and N and P

\hspace{-16}$Is There is any Relation exists b/w the angle $\bf{M\;\;,N}$ and $\bf{P}$ Such \\\\ that $\bf{\cos^2(M)+\cos^2(N)+\cos^2(P)+2.\cos(M).\cos(N).\cos(P)=1}$

#Mathematics #Trignometry

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Ketan Chandak ·2012-05-20 21:31:42

i guess they are angles of a triangle....M+N+P=180

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rahul ·2012-05-23 12:41:03

ya...

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.........!!

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Relation b/w M and N and P

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