In a □ ABC , a = 5 , b = 4 and cos ( A − B ) = 32 31 , then c must be

cos ( A − B ) = 1 + t a n 2 ( 2 A − B ) 1 − t a n 2 ( 2 A − B ) = tan ( 2 A − B ) = 63 1 Use Napier's analogy, we will get cot 2 C = 63 9 Then cos C = 8 1 , c = 6

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MathematicsTrigonometric Ratios & IdentitiesMiscellaneous/MixedMedium2 minQB

MathematicsMediuminteger

In $a □ ABC, a = 5, b = 4$ and $cos (A - B) = \frac{31}{32}$ , then c must be

Answer:

Solution:

$cos (A - B) = \frac{1 - t a n ^{2} ( \frac{A - B}{2} )}{1 + t a n ^{2} ( \frac{A - B}{2} )} = tan (\frac{A - B}{2}) = \frac{1}{63}$

Use Napier's analogy, we will get $cot \frac{C}{2} = \frac{9}{63}$

Then $cos C = \frac{1}{8}, c = 6$

Stream:JEESubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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