Question

The numerical value of (tan 20° + tan 40° + V3 tan 20° tan 40")
must be​

Answer 1

Step-by-step explanation:

tan

20

∘

+

tan

40

∘

+

√

3

tan

20

∘

tan

40

∘

=

a

.

√

3

4

,

b

.

√

3

2

,

c

.

√

3

,

d

.

1

Answer 2

$\huge{\mathbb{\red{ANSWER:-}}}$

$\sf{tan60 = tan(20 + 40)}$

$\sf{tan(20+40)=\dfrac{tan20+ tan40}{1 - tan20tan40}}$

$\sf{\small\boxed{tan(A+B)=\dfrac{tanA + tanB}{1-tanAtanB}}}$

$\sf{tan60 =\dfrac{tan20 + tan40}{1 - tan20tan40}}$

$\sf{\sqrt{3}=\dfrac{tan20 + tan40}{1 - tan20tan40}}$

$\sf{\sqrt{3}(1 - tan20tan40)=tan20 + tan40}$

$\sf{\sqrt{3} - \sqrt{3} tan20tan40 = tan20 + tan40}$

$\sf{tan20 + tan40 + \sqrt{3} tan20tan40 =\sqrt{3}}$