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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 36 of 61
Marks: +1, -0
sin⁡x+sin⁡3xcos⁡x+cos⁡3x\frac{\sin x + \sin 3x}{\cos x + \cos 3x} = tan 2x
Solution:  
We have, L.H.S.= sin⁡x+sin⁡3xcos⁡x+cos⁡3x\frac{\sin x + \sin 3x}{\cos x + \cos 3x}
= 2sin⁡(x+3x2)cos⁡(x−3x2)2cos⁡(x+3x2)cos⁡(x−3x2)\frac{2 \sin\left(\frac{x+3x}{2}\right) \cos\left(\frac{x-3x}{2}\right)}{2 \cos\left(\frac{x+3x}{2}\right) \cos\left(\frac{x-3x}{2}\right)} = 2sin⁡2xcos⁡x(−x)2cos⁡2xcos⁡(−x)\frac{2 \sin 2x \cos x (-x)}{2 \cos 2x \cos(-x)} = tan 2x = R.H.S.
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