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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
5 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
5 years ago
xy+yz+zx+1thenx/1+x2+y/1+y2+z/1+zPease sent me answer this problem
Ansh Goyal
29 Points
one year 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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