Simplify: cos(x)/1+sin(x)+sin(x)/1+cos(x).

Correct Answer is : cos(x)+sin(x)+1(1+sin(x))(1+cos(x))cos(x)+sin(x)+1/(1+sin(x))(1+cos(x))(1+sin(x))(1+cos(x))cos(x)+sin(x)+1

Correct Answer is : cos(x)+sin(x)+1(1+sin(x))(1+cos(x))cos(x)+sin(x)+1/(1+sin(x))(1+cos(x))(1+sin(x))(1+cos(x))cos(x)+sin(x)+1

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SSC CHSL 13 Nov 2025 Shift 3 Paper

Question : 75 of 100

Marks: +1, -0

Simplify:

\frac{cos(x)}{1+sin(x)}+\frac{sin(x)}{1+cos(x)}

Solution:

Concept:

Use the formula for adding fractions:

\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}

and the identity

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

Explanation:

Step 1: Write the sum with a common denominator:

\frac{\cos x}{1+\sin x}+\frac{\sin x}{1+\cos x} = \frac{\cos x(1+\cos x)+\sin x(1+\sin x)}{(1+\sin x)(1+\cos x)}

Step 2: Expand the numerator:

\cos x+\cos^2 x+\sin x+\sin^2 x

Step 3: Rearrange terms:

(\sin^2 x+\cos^2 x) + (\sin x+\cos x)

Step 4: Use

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

to get:

1+\sin x+\cos x

Step 5: Place over the common denominator:

\frac{1+\sin x+\cos x}{(1+\sin x)(1+\cos x)}

Answer:

\frac{\cos x+\sin x+1}{(1+\sin x)(1+\cos x)}

(Option D)

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