Question:
The value of (1 – tan215o)/(1 + tan215o) is
A. 1
B. √3
C. √3/2
D. 2
Solution:
C. √3/2
Explanation:
According to the question,
Let θ = 15° ⇒ 2θ = 30°
Now, since we know that,
$\cos 2 \theta=\frac{1-\tan ^{2} \theta}{1+\tan ^{2} \theta}$
$\Rightarrow \cos 30^{\circ}=\frac{1-\tan ^{2} 15^{\circ}}{1+\tan ^{2} 15^{\circ}}$
$\Rightarrow \frac{\sqrt{3}}{2}=\frac{1-\tan ^{2} 15^{\circ}}{1+\tan ^{2} 15^{\circ}}$
Thus, option (C) √3/2 is the correct answer.
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