InterviewSolution
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InterviewSolution
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सिद्ध कीजिए `tan^(-1)sqrt(x)=(1)/(2)cos^(-1) ""((1-x)/(1+x)), x in [0,1]` |
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Answer» Putting, `x=tan^(2)theta`, we get RHS `=1/2cos^(-1)(1-x)/(1+x)` `=1/2cos^(-1)((1-tan^(2)theta)/(1+tan^(2)theta))` `=1/2cos^(-1)(cos2theta)` `=(1/2 xx 2theta) = theta=tan^(-1)sqrt(x)`= LHS `[therefore x=tan^(2)theta rArr tantheta=sqrt(x) rArr theta=tan^(-1)sqrt(x)]` Hence, `tan^(-1)=1/2cos^(-1)((1-x)(1+x))`. |
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