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JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

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Application +4 | -1
If x+y−z+xyz=0x+y-z+x y z=0, then 2x1−x2+2y1−y2−2z1−z2\frac{2 x}{1-x^2}+\frac{2 y}{1-y^2}-\frac{2 z}{1-z^2} is equal to
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Correct option: C
8xyz[(1−x2)(1−y2)(1−z2)]\frac{8 x y z}{\left[\left(1-x^2\right)\left(1-y^2\right)\left(1-z^2\right)\right]}
Option C (8xyz[(1−x2)(1−y2)(1−z2)]\frac{{8 x y z}}{{\left[(1-x^2)(1-y^2)(1-z^2)\right]}}) is correct because by substituting x=tan⁡Ax = \tan A, y=tan⁡By = \tan B, and −z=tan⁡C-z = \tan C and using trigonometric identities, the expression simplifies to the given form.

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