Simplified expression of 1- ² y/1+ y+1+ y/ y- y/1- y is :

Correct Answer is : cos⁡y ycosy

Correct Answer is : cos⁡y ycosy

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COMEDK 2025 Afternoon Solved Paper

Question : 141 of 180

Marks: +1, -0

1-\frac{\sin ^2 y}{1+\cos y}+\frac{1+\cos y}{\sin y}-\frac{\sin y}{1-\cos y}

is :

Solution:

Concept:

Use trigonometric identities to simplify the given expression step by step.

Explanation:

Let

E = 1 - \frac{\sin^2 y}{1+\cos y} + \frac{1+\cos y}{\sin y} - \frac{\sin y}{1-\cos y}

First, simplify the first two terms:

1 - \frac{\sin^2 y}{1+\cos y}

Use

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

Then

\frac{\sin^2 y}{1+\cos y} = \frac{1-\cos^2 y}{1+\cos y} = 1 - \cos y

1 - (1 - \cos y) = \cos y

Now simplify the remaining pair:

\frac{1+\cos y}{\sin y} - \frac{\sin y}{1-\cos y}

Using identities,

\frac{1+\cos y}{\sin y} = \cot\frac{y}{2}

and

\frac{\sin y}{1-\cos y} = \cot\frac{y}{2}

Thus their difference is

0

Therefore

E = \cos y + 0 = \cos y

Answer:

Option B.

\cos y

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