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Complete the identity. cos (alpha - beta)/cos alpha cos beta = ?

A1 + cot α cot β
Btan α tan β + cot β
C1 + tan α tan β
D1 + cot α tan β

Verified Answer :

i belive the answer to be b

Ozgr

\(\frac{cos(a-b)}{cos(a)cos(b)} = \frac{cos(a)cos(b)+sin(a)sin(b)}{cos(a)cos(b)} = 1+ \frac{sin(a)sin(b)}{cos(a)cos(b)} =1+tan(a)tan(b)\)

Note that I used these identities :\(cos(a-b)=cos(a)cos(b)+sin(a)sin(b)\) and  \(tan(a)= \frac{sin(a)}{cos(a)}\)

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