InterviewSolution
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InterviewSolution
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dy/dxज्ञात कीजिए y=`cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))]` |
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Answer» माना `y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))]` अब `" "sqrt(1+sinx)=sqrt(sin^(2).(x)/(2)cos^(2).(x)/(2)+2sin.(x)/(2)cos.(x)/(2))` `" "=sqrt((sin.(x)/(2)+cos.(x)/(2))^(2))=sin.(x)/(2)+cos.(x)/(2)` `sqrt(1-sinx)=sqrt(sin^(2).(x)/(2)+cos^(2).(x)/(2)-2sin.(x)/(2)cos.(x)/(2))` तथा `" "=sqrt((cos.(x)/(2)-sin.(x)/(2))^(2))=cos.(x)/(2)-sin.(x)/(2)` `" "(because 0 lt xlt (pi)/(2))` `therefore" "y=cot^(-1)[((sin.(x)/(2)+cos.(x)/(2))+(cos.(x)/(2)-sin.(x)/(2)))/((sin.(x)/(2)+cos.(x)/(2))-(cos.(x)/(2)-sin.(x)/(2)))]` `=cot^(-1)((2cos.(x)/(2))/(2sin.(x)/(2)))=cot^(-1)(cot.(x)/(2))=(x)/(2)` `rArr" "(dy)/(dx)=(d)/(dx)((x)/(2))=(1)/(2)` |
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