Question

if tan alpha = 1/11 , tan beta = 5/6 prove that alpha + beta = 45°​

Answer 1

Answer:

Refer the attached picture.

Answer 2

$\bigstar$$\boxed{\huge{\red{\mathfrak{Question}}}}$$\bigstar$

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$tan \: \alpha = \frac{1}{11} \\ tan \: \beta = \frac{5}{6}$

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$\mathtt{\blue{\underline{\underline{To\:prove:}}}}$

$\alpha + \beta = 45°$

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$\mathtt{\green{\underline{\underline{Solution:}}}}$

Tan A → 5/6 ----------( Given )

Tan B → 1/11 -----------( Given )

We know that :

$tan( \alpha + \beta ) = \frac{tan \: \alpha \: + tan \: \beta }{1 - tan \: \alpha .tan \: \beta }$

Put these values in it :

$tan( \alpha + \beta ) = \frac{ \frac{5}{6} + \frac{1}{11} }{1 - \frac{5}{6} . \frac{1}{11} }$

$tan( \alpha + \beta ) = \frac{ \frac{55 + 6}{66} }{ \frac{66 - 5}{66} }$

$tan( \alpha + \beta )= \frac{ \frac{61}{66} }{ \frac{61}{66} }$

$tan( \alpha + \beta ) = 1$

We know that ,

Tan 45° = 1

$tan( \alpha + \beta ) = tan \: 45° \\ \\ \alpha + \beta = 45°$

$\mathfrak{\huge{Hence\:Proved}}$