If cos⁡x+cos⁡y=45,cos⁡x−cos⁡y=27, then 14tan⁡x−y2+5cot⁡x+y2=

cos⁡x+cos⁡ycos⁡x−cos⁡y=145⇒2cos⁡x+y2cos⁡x−y2−2sin⁡x+y2sin⁡x−y2=145⇒14tan⁡x−y2+5cot⁡x+y2=0

If cos⁡x+cos⁡y=45,cos⁡x−cos⁡y=27, then 14tan⁡x−y2+5cot⁡x+y2=

cos⁡x+cos⁡ycos⁡x−cos⁡y=145⇒2cos⁡x+y2cos⁡x−y2−2sin⁡x+y2sin⁡x−y2=145⇒14tan⁡x−y2+5cot⁡x+y2=0

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$If \cos x + \cos y = \frac{4}{5}, \cos x - \cos y = \frac{2}{7}, then 14 \tan (\frac{x - y}{2}) + 5 \cot (\frac{x + y}{2}) =$

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Detailed Solution

$\frac{\cos x + \cos y}{\cos x - \cos y} = \frac{14}{5} \Rightarrow \frac{2 \cos (\frac{x + y}{2}) \cos (\frac{x - y}{2})}{- 2 \sin (\frac{x + y}{2}) \sin (\frac{x - y}{2})} = \frac{14}{5} \Rightarrow 14 \tan (\frac{x - y}{2}) + 5 \cot (\frac{x + y}{2}) = 0$