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Question
If a = b \[\cos \frac{2\pi}{3} = c \cos\frac{4\pi}{3}\] then write the value of ab + bc + ca.
Solution
\[a = b \cos120°= c \cos 240°\]
\[ \Rightarrow a = - \frac{1}{2}b = - \frac{1}{2}c\]
\[\text{ Therefore }, \]
\[ab + bc + ca = \frac{- 1}{2}b \times b + b \times b + b \times \frac{- 1}{2}b\]
\[ = - b^2 + b^2 \]
\[ = 0\]
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