In any △ ABC , which is not right angled, ∑ cos A cosec B cosec C is

∑ s i n B s i n C c o s A = ∑ s i n B s i n C − c o s ( B + C ) = ∑ ( 1 − cot B cot C ) = 3 − ∑ cot A cot B = 3 − 1 = 2 , a constant

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MathematicsTrigonometric Ratios & IdentitiesConditional identitiesMedium2 minQB

MathematicsMediumsingle choice

In any $△ ABC$ , which is not right angled, $\sum cos A cosec B cosec C$ is

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Solution:

$\sum \frac{c o s A}{s i n B s i n C} = \sum \frac{- c o s ( B + C )}{s i n B s i n C} = \sum (1 - cot B cot C) = 3 - \sum cot A cot B = 3 - 1 = 2$ , a constant

Stream:JEESubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Conditional identities

⏱ 2mℹ️ Source: QB

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