Question

tan40+tan80-√3tan40tan80

Answer 1

Using the Trigonometry Identity,
$tan ( a + b) = \frac{tan \: a + tan \: b}{1 - tan \: a.tan \: b}$
As,
120 = 80 + 40

=>
$tan (120) = tan(80 + 40) = \frac{tan \: 80 + tan \: 40}{1 - tan \: 80.tan \: 40}$

As, tan 120 = -√3.

$- \sqrt{3} = \frac{tan \: 80 + tan \: 40}{1 - tan \: 80.tan \: 40}$
$- \sqrt{3} \times (1 - tan \: 80.tan \: 40) = tan \: 80 + tan \: 40$
On Simplifying, we get

$tan \: 40 + tan \: 80 - \sqrt{3}.tan \: 40.tan \: 80 = - \sqrt{3}$

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Answer 2

Step-by-step explanation:

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