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torisob [31]
2 years ago
10

If A+B= 45° then prove that: tanA+ tanB+ tanA. tanB​

Mathematics
1 answer:
Iteru [2.4K]2 years ago
8 0

Answer:

See Explanation

Step-by-step explanation:

A+B= 45 \degree \\  \\ assuming  \:  \tan \: on \: both \: sides \\  \\\implies \: \tan( A+B)=  \tan 45 \degree \\  \\  \implies \: \tan( A+B)=  1 \:  \: \\  (  \because \: \tan 45 \degree = 1) \\  \\ \implies \:  \frac{\tan \: A +\tan \: B }{1 - \tan \: A .\tan \: B }  = 1 \\  \\ \implies \: \tan \: A +\tan \: B = 1 - \tan \: A .\tan \: B \\  \\ \purple{ \implies }\:  \orange{ \bold{\tan \: A +\tan \: B  + \tan \: A .\tan \: B= 1 }} \\  \\ thus \: proved

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