The value of the expression 1 - frac{sin^2 y} | vedclass

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(D) Given expression: $E = 1 - \frac{\sin^2 y}{1 + \cos y} + \frac{1 + \cos y}{\sin y} - \frac{\sin y}{1 - \cos y}$Step $1$: Simplify the first two te

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$\cos y$

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(D) Given expression: $E = 1 - \frac{\sin^2 y}{1 + \cos y} + \frac{1 + \cos y}{\sin y} - \frac{\sin y}{1 - \cos y}$Step $1$: Simplify the first two terms:$1 - \frac{\sin^2 y}{1 + \cos y} = \frac{1 + \cos y - (1 - \cos^2 y)}{1 + \cos y} = \frac{\cos y + \cos^2 y}{1 + \cos y} = \frac{\cos y(1 + \cos y)}{1 + \cos y} = \cos y$Step $2$: Simplify the last two terms:$\frac{1 + \cos y}{\sin y} - \frac{\sin y}{1 - \cos y} = \frac{(1 + \cos y)(1 - \cos y) - \sin^2 y}{\sin y(1 - \cos y)} = \frac{1 - \cos^2 y - \sin^2 y}{\sin y(1 - \cos y)} = \frac{\sin^2 y - \sin^2 y}{\sin y(1 - \cos y)} = 0$Step $3$: Combine the results:$E = \cos y + 0 = \cos y$

The value of the expression $1 - \frac{\sin^2 y}{1 + \cos y} + \frac{1 + \cos y}{\sin y} - \frac{\sin y}{1 - \cos y}$ is equal to

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