Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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If a = B Cos 2 π 3 = C Cos 4 π 3 Then Write the Value of Ab + Bc + Ca. - Mathematics

Short Note

If a = b \[\cos \frac{2\pi}{3} = c \cos\frac{4\pi}{3}\] then write the value of ab + bc + ca.  

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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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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 7 Values of Trigonometric function at sum or difference of angles
Q 9 | Page 27
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