InterviewSolution
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InterviewSolution
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If `tan^(-1)(a/x)+tan^(-1)(b/x)+tan^(-1)(c /x)+tan^(-1)(d/x)=(pi)/(2)` then `x^(4)-x^(2)(Sigma ab)+abcd=`A. `-1`B. 0C. 1D. 2 |
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Answer» We have `tan^(-1)(a)/(x)+tan^(-1)(b)/(x)+tan^(-1)(c )/(x)+tan^(-1)(d)/(x)=(pi)/(2)` `rarr tan^(-1)(a)/(x)+tan^(-1)(b)/(x)=(pi)/(2)-{tan^(-1)(c )/(x)+tan^(-1)(d)/(x)}` `rarr tan^(-1) ((a+b)x)/(x^(2)-ab)=(pi)/(2)-tan^(-1)((c+d)x)/(x^(2)-cd)` `rarr tan^(-1)((a+b)x)/(x^(2)-ab)=co^(-1)((c+d)x)/(x^(2)-cd)` `rarr tan^(-1)((a+b)x)/(x^(2)-ab)=(x^(2)-cd)/((c+d)x) rarr x^(4) -x^(2) (Sigma ab)+abcd=0` |
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