In triangle ABC, the value of the expression ∑ r = 0 n n C r a r b n − r cos ( r B − ( n − r ) A ) is equal to

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MathematicsTrigonometric Ratios & IdentitiesSummation of SeriesMedium2 minQB

MathematicsMediumsingle choice

In triangle ABC, the value of the expression $\sum_{r = 0}^{n}^{n} C_{r} a^{r} b^{n - r} cos (r B - (n - r) A)$ is equal to

Answer:

Solution:

It is the real part of the expansion of $(a e^{i B} + b e^{- i A})^{n}$ , i.e. of $(a cos B + b cos A)^{n} = c^{n}$ .

Stream:JEESubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Summation of Series

⏱ 2mℹ️ Source: QB

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