1 - tan 2 15 ° 1 + tan 2 15 ° =, 1, 3, 3 2, 2

We know that cos 2 θ = 1 - tan 2 θ 1 + tan 2 θ . Hence, 1 - tan 2 15 ° 1 + tan 2 15 ° = cos 30 ° ⇒ 1 - tan 2 15 ° 1 + tan 2 15 ° = 3 2 .

1 - tan 2 15 ° 1 + tan 2 15 ° =

Question: Answered & Verified by Expert

\frac{1 - \tan^{2} 15 °}{1 + \tan^{2} 15 °} =

MathematicsTrigonometric Ratios & IdentitiesTS EAMCETTS EAMCET 2021 (05 Aug Shift 1)

Options:

Solution:

2295 Upvotes Verified Answer

The correct answer is:

\frac{\sqrt{3}}{2}

We know that $\cos 2 θ = \frac{1 - \tan^{2} θ}{1 + \tan^{2} θ} .$

Hence, $\frac{1 - \tan^{2} 15 °}{1 + \tan^{2} 15 °} = \cos 30 °$

$\Rightarrow \frac{1 - \tan^{2} 15 °}{1 + \tan^{2} 15 °} = \frac{\sqrt{3}}{2} .$

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