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NCERT Class XI Mathematics - Trigonometric Functions - Solutions

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Question : 34 of 61
Marks: +1, -0
sin⁡5x+sin⁡3xcos⁡5x+cos⁡3x\frac{\sin5x+\sin3x}{\cos5x+\cos3x} = tan 4x
Solution:  
We have, L.H.S.= sin⁡5x+sin⁡3xcos⁡5x+cos⁡3x\frac{\sin5x+\sin3x}{\cos5x+\cos3x}
= 2sin⁡(5x+3x2)cos⁡x(5x−3x2)2cos⁡(5x+3x2)cos⁡(5x−3x2)\frac{2\sin\left(\frac{5x+3x}{2}\right)\cos x\left(\frac{5x-3x}{2}\right)}{2\cos\left(\frac{5x+3x}{2}\right)\cos\left(\frac{5x-3x}{2}\right)} = 2sin⁡4xcos⁡x2cos⁡4xcos⁡x\frac{2\sin4x\cos x}{2\cos4x\cos x} = tan 4x = R.H.S.
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