If a x = b , b y = c , and c z = a for positive real variables, evaluate x yz ∑ r = 1 89 l o g 10 t a n ( π r /180 ) .

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MathematicsTrigonometric Ratios & IdentitiesSummation of SeriesMedium3 minQB

MathematicsMediuminteger

If $a^{x} = b, b^{y} = c$ , and $c^{z} = a$ for positive real variables, evaluate $\frac{\sum _{r = 1}^{89} l o g _{10} t a n ( π r /180 )}{x yz}$ .

Answer:

Solution:

Pair $r$ with $90 - r$ . Since $tan u tan (π /2 - u) = 1$ , each paired logarithmic sum is zero.

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

⏱ 3mℹ️ Source: QB

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