InterviewSolution
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InterviewSolution
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Statement -1: If `xltsqrt(e )`then `cot^(-1){log(e//x^(2))/log(ex^(2))}+cot^(-1){log(ex^(4))/log(e^(2)//x^(2)))}=pi-tan^(-1)3` statement 2:`tan^(-1)(x+y)/(1-xy)=tan^(-1)x+tan^(-1)y if xylt1`A. Statement-1 is is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True. |
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Answer» statement 2 is true (see history ) Now `cot^(-1){log(e//x^(1))/log(ex^(2))}+cot^(-1){logex^(4))/log(e^(2)//x^(2)))}` `=cot^(-1){(1-2logx)/(1+2 logx)}+cot^(-1){(1+4logx)/(2-2logx)}` `=tan^(-1)(1+2 logx)/(1-23logx)+(pi)/(2)tan^(-1)((1/2+2logx)/(1-1/2xx2logx)` `=tan^(-1)(1+2logx)/(1-2logx)+(pi)/(2)-tan^(-1)((1/2+2logx)/(1-1/2xx2logx))` `=tan^(-1)(1)+tan^(-1)(2 logx)+(pi)/(2)-tan^(-1)1/2-tan^(-1)(2 logx)` if `2 log x l 1 and log x lt 1` `=(3pi)/(4) -tan^(-1)1/2 if x lt sqrt(e )` `=pi -(tan^(-1)1+tan^(-1)1/2)=pi tan^(-1)3` So statement 1 is alos true also statement -2 is a correct explanation fro statement-1 |
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