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  4. The value of the expression 1 - ( sin2 y /1 + cos y) + (1+ cos y/ sin y ) - ( sin y/1- cos y) is equal to

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Q. 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

Trigonometric Functions

Solution:

$1 - \frac{\sin^{2} y }{1 + \cos y} + \frac{1+ \cos y}{\sin y } - \frac{\sin y}{1- \cos y} $
$=1 - \left(\frac{1-\cos^{2} y}{1+ \cos y}\right) + \frac{1-\cos^{2} y - \sin^{2}y}{\sin y \left(1-\cos y\right)} $