Question

prove that :
(1 + tan 24°) (1 + tan 21°) (1 + tan 23°) (1 + tan 22°) = 4​

Answer 1

$\implies if\: \: \: \: \alpha + \beta = 45 \degree \: \\ \\ then\\ \\ \implies (1 + \tan \: \alpha )(1 + \tan \beta ) = 2 \\ \\ \implies \: (1 + \tan24)(1 + \tan \: 21) \\ (1 + \tan \: 23)(1 + \tan \: 22) \\ \\ \implies \: 2 \times 2 \\ \\ \implies \: 4 \: hence \: proved$

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