For α = 13 2 π , cos α cos 5 α + cos 2 α cos 3 α + cos 4 α cos 6 α =

= 2 1 [ cos 6 α + cos 4 α + cos 5 α + cos α + cos 10 α + cos 2 α ] and 10 α = 2 π − 3 α , so the bracket is cos α + … + cos 6 α = − 2 1 . The value is 2 1 ( − 2 1 ) = − 4 1 .

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Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

MathematicsTrigonometric Ratios & IdentitiesSummation of SeriesMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

To evaluate an expression of the form $sin a + sin (a + d) + \dots + sin (a + (n - 1) d)$ or $cos a + cos (a + d) + \dots + cos (a + (n - 1) d)$ we can multiply each term by $2 sin \frac{d}{2}$ and apply the transformation formula to the resulting products. Using this information, answer the following.

For $α = \frac{2 π}{13}$ , $cos α cos 5 α + cos 2 α cos 3 α + cos 4 α cos 6 α =$

Options:

Answer:

Solution:

$= \frac{1}{2} [cos 6 α + cos 4 α + cos 5 α + cos α + cos 10 α + cos 2 α]$ and $10 α = 2 π - 3 α$ , so the bracket is $cos α + \dots + cos 6 α = - \frac{1}{2}$ . The value is $\frac{1}{2} (- \frac{1}{2}) = - \frac{1}{4}$ .

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

⏱ 2mℹ️ Source: QB

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