Question

(1+tan20°)(1+tan25°)

Answer 1

(1+tan20)(1+tan25) 
= 1 + tan20 + tan25 + tan20tan25 
= 1 + tan45 * (1 - tan20tan25) + tan20tan25 
= 1 + 1(1 - tan20tan25) + tan20tan25 
= 2. 

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Answer 2

Answer:

2

Step-by-step explanation:

$(1+tan a)(1+tan b)= 2+tan a + tan b -\frac{tana+tanb}{tan(a+b)}$.......(1)

$tana=tan20^{o} \\tanb=tan25^{o}$

Inserting the value in equation (1), we get:

$(1+tan a)(1+tan b)= 2+tan 20 + tan25 -\frac{tan20+tan25}{tan(20+25)}$

$= 2+tan 20 + tan25 -\frac{tan20+tan25}{tan(45)}$

$= 2+tan 20 + tan25 -\frac{tan20+tan25}{1} (since, tan45^{o}=1 )$

$= 2+tan 20 + tan25 -(tan 20 + tan25)$

$=2$

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