Find the value of 1 − t a n 2 30 ∘ 1 + t a n 2 30 ∘ . Options: A . &nbsp 0.5 B . &nbsp 1 C . &nbsp 2 D . &nbsp 4

Answer: Option A : A We know that t a n 30 ∘ = 1 √ 3 . ⇒ 1 − t a n 2 30 ∘ 1 + t a n 2 30 ∘ = 1 − ( 1 √ 3 ) 2 1 + ( 1 √ 3 ) 2 = 1 − ( 1 3 ) 1 + ( 1 3 ) = 3 − 1 3 + 1 = 2 4 = 1 2 = 0.5

Find the value of 1−tan2 30∘1+tan2 30∘.

Question

Find the value of $\frac{1 - t a n^{2} 30^{\circ}}{1 + t a n^{2} 30^{\circ}} .$

Options:

A . 0.5

B . 1

C . 2

D . 4

Answer: Option A
:
A

$We know that t a n 30^{\circ} = \frac{1}{\sqrt{3}} .$

$\Rightarrow \frac{1 - t a n^{2} 30^{\circ}}{1 + t a n^{2} 30^{\circ}} = \frac{1 - (\frac{1}{\sqrt{3}})^{2}}{1 + (\frac{1}{\sqrt{3}})^{2}}$

$= \frac{1 - (\frac{1}{3})}{1 + (\frac{1}{3})}$

$= \frac{3 - 1}{3 + 1}$

$= \frac{2}{4}$ = $\frac{1}{2} = 0.5$

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