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if a line makes A,B,C angles with coordinates axes, prove cos2A+cos2B+cos2c+1=0

if a line makes A,B,C angles with coordinates axes, prove cos2A+cos2B+cos2c+1=0

Grade:12

1 Answers

jagdish singh singh
173 Points
5 years ago
\hspace{-0.6 cm }$Using Direction Cosine formula $\bf{\cos^2A+\cos^2 B+cos^2 C= 1}$\\\\ Now Using $\bf{1+ \cos 2A=2\cos^2A\;, }$ We get \\\\ So $\bf{2\cos^2A+2\cos^2 B+2cos^2 C= 2}$\\\\So $\bf{1+\cos 2A+1+\cos 2B+1+\cos 2C = 2}$\\\\ So $\bf{\cos 2A+\cos 2B+\cos 2C+1 =0}$

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