NIMCET 2011 — Mathematics PYQ

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Question

NIMCET 2011 — Mathematics PYQ

NIMCET | Mathematics | 2011

The value of $\frac{1-\tan^2 15^\circ}{1+\tan^2 15^\circ}$ is:

Choose the correct answer:

Explanation

1. Recall the identity:

The formula for $\cos 2\theta$ in terms of $\tan \theta$ is:

\cos 2\theta = \frac{1-\tan^2 \theta}{1+\tan^2 \theta}

2. Apply the identity to the given expression:

In this problem, $\theta = 15^\circ$ .

\frac{1-\tan^2 15^\circ}{1+\tan^2 15^\circ} = \cos(2 \times 15^\circ)

3. Simplify the angle:

\cos(30^\circ)

4. Substitute the standard value:

From the trigonometric table, we know:

\cos 30^\circ = \frac{\sqrt{3}}{2}

Conclusion:

The value of the expression is $\frac{\sqrt{3}}{2}$ .

The correct option is (c).

Choose the correct answer:

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