InterviewSolution
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InterviewSolution
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If `|a|lt1| b|lt1and|x|lt1` then the solution of `sin^(-1)((2a)/(1+a^(2)))-cos^(-1)((1-b^(2))/(1+b^(2)))=tan^(-1)((2x)/(1-x^(2)))` isA. `(a-b)/(1-ab)`B. `(1+ab)/(a-b)`C. `(ab-1)/(a+b)`D. `(a-b)/(a+ab)` |
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Answer» We have `sin^(-1)(2a)/(1+a^(2))-cos^(-1)(1-b^(2))/(1+b^(2))=tan^(-1)(2x)/(1-x^(2))` `rarr 2tan^(-1)a-2tan^(-1)b=2tan^(-1)x` `rarr tan^(-1)a-tan^(-1)b=tan^(-1)x` `rarr tan^(-1)x=tan^(-1)(a-b)/(1+ab)` `rarr x=(a-bb)/(1+ab)` |
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