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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 35 of 61
Marks: +1, -0
sin⁡x−sin⁡ycos⁡x+cos⁡y\frac{\sin x - \sin y}{\cos x + \cos y} = tan (x−y2)\left(\frac{x-y}{2}\right)
Solution:  
We have, L.H.S.= sin⁡x−sin⁡ycos⁡x+cos⁡y\frac{\sin x - \sin y}{\cos x + \cos y}
= 2cos⁡(x+y2)sin⁡(x−y2)2cos⁡(x+y2)cos⁡(x−y2)\frac{2\cos\left(\frac{x+y}{2}\right)\sin\left(\frac{x-y}{2}\right)}{2\cos\left(\frac{x+y}{2}\right)\cos\left(\frac{x-y}{2}\right)} = sin⁡(x−y2)cos⁡(x−y2)\frac{\sin\left(\frac{x-y}{2}\right)}{\cos\left(\frac{x-y}{2}\right)} = tan (x−y2)\left(\frac{x-y}{2}\right) = R.H.S.
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