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# if cosx + cosy=4/5 and cosx - cosy=2/7 prove that 14tan(x-y/2)+5cot(x+y/2)=0

Lab Bhattacharjee
121 Points
5 years ago
$\text{Prosthaphaeresis Formulas}\\ \cos x+\cos y=2\cos\dfrac{x+y}2\cos\dfrac{x-y}2\\ \text{ and } \cos x-\cos y=-2\sin\dfrac{x+y}2\sin\dfrac{x-y}2$$\text{Using Prosthaphaeresis Formulas}\\ \cos x+\cos y=2\cos\dfrac{x+y}2\cos\dfrac{x-y}2\\ \text{ and } \cos x-\cos y=-2\sin\dfrac{x+y}2\sin\dfrac{x-y}2$
girish
14 Points
5 years ago
adding both you get cosx subtracting cosy so we also got sinx and siny if we use half angle formulas we can write sinx in terms of tanx/2 so we got that too so we can solve
Gowri sankar
292 Points
5 years ago
This question solve using half angle formulas we can write sinx in terms of tanx/2 so we got that then solve this problem.