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If xy + yz + zx = 1 show that [x/(1 - x^2)] + [y/(1 - y^2)] + [z/(1 - z^2)] = (4xyz)/[(1 - x^2)(1 - y^2)(1 - z^2)]

If xy + yz + zx = 1
show that
[x/(1 - x^2)] + [y/(1 - y^2)] + [z/(1 - z^2)] = (4xyz)/[(1 - x^2)(1 - y^2)(1 - z^2)]

Grade:11

3 Answers

Lab Bhattacharjee
121 Points
8 years ago
\text{ Let } x=\tan A\text{ etc.} \\ \implies \tan(A+B+C)=\infty\implies A+B+C=n\pi+\dfrac\pi2 \text{ where } n \text{ is any integer} \\ \implies 2A+2B+2C=2n\pi+\pi \\ \implies\tan2A+\tan2B+\tan2C=\tan2A\tan2B\tan2C \\ \text{ Now use } \tan2D=\dfrac{2\tan D}{1-\tan^2D}
siddareddy
13 Points
8 years ago
xy+yz+zx+1thenx/1+x2+y/1+y2+z/1+z2 Pease sent me answer this problem
Ansh Goyal
29 Points
4 years ago
just take the lcm of the l.h.s. and start solving. by taking xyz, x,y,z, common respectively, you will get the answer
 

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