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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 33 of 61
Marks: +1, -0
cos⁡9x−cos⁡5xsin⁡17x−sin⁡3x\frac{\cos 9x - \cos 5x}{\sin 17x - \sin 3x} = - sin⁡2xcos⁡10x\frac{\sin 2x}{\cos 10x}
Solution:  
We have, L.H.S = cos⁡9x−cos⁡5xsin⁡17x−sin⁡3x\frac{\cos 9x - \cos 5x}{\sin 17x - \sin 3x}
= −2sin⁡(9x+5x2)sin⁡(9x−5x2)2sin⁡(17x−3x2)cos⁡(17x+3x2)\frac{-2 \sin\left(\frac{9x+5x}{2}\right) \sin\left(\frac{9x-5x}{2}\right)}{2 \sin\left(\frac{17x-3x}{2}\right) \cos\left(\frac{17x+3x}{2}\right)} = −2sin⁡7xsin⁡2x2sin⁡7xcos⁡10x\frac{-2 \sin 7x \sin 2x}{2 \sin 7x \cos 10x} = −sin⁡2xcos⁡10x\frac{-\sin 2x}{\cos 10x} = R.H.S.
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