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SSC CHSL 14 Nov 2025 Shift 2 Paper

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Question : 71 of 100

Marks: +1, -0

Simplify the expression:

\frac{cos^{2}(x)-sin^{2}(x)}{1-sin^{2}(x)}

.

$tan^{2}(x)$
1
$1-tan^{2}(x)$
$1-tan2(x)$

Solution:

Concept:

Use the identities

\cos^2 x - \sin^2 x = \cos 2x

and

1 - \sin^2 x = \cos^2 x

to simplify the fraction.

Explanation:

Start with

\frac{\cos^2 x - \sin^2 x}{1 - \sin^2 x}

.

Replace

1 - \sin^2 x

with

\cos^2 x

.

The expression becomes

\frac{\cos^2 x - \sin^2 x}{\cos^2 x}

.

Separate the numerator:

\frac{\cos^2 x}{\cos^2 x} - \frac{\sin^2 x}{\cos^2 x}

.

Simplify each term:

1 - \tan^2 x

.

Answer:

C.

1 - \tan^2 x

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