InterviewSolution
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InterviewSolution
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निम्नलिखित समीकरणों को हल कीजिए - `tan^(-1)x+2cot^(-1)x=(2pi)/(3).` |
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Answer» दिया गया समीकरण है - `tan^(-1)x+2cot^(-1)x=(2pi)/(3)` `rArr" "tan^(-1)x+2tan^(-1)((1)/(x))=(2pi)/(3),` `" "[because cot^(-1)x=tan^(-1).(1)/(x)]` `rArr" "tan^(-1)x+tan^(-1)((2xx+(1)/(x))/(1-(1)/(x^(2))))=(2pi)/(3)` `rArr" "tan^(-1)x+tan^(-1)(((2)/(x))/((x^(2)-1)/(x^(2))))=(2pi)/(3)` `rArr" "tan^(-1)x+tan^(-1)((2x)/(x^(2)-1))=(2pi)/(3)` `rArr" "tan^(-1)((x+(2x)/(x^(2)-1))/(1-x xx(2x)/(x^(2)-1)))=(2pi)/(3)` `rArr" "tan^(-1)((x^(3)+x)/(-1-x^(2)))=(2pi)/(3)` `rArr" "(x^(3)+x)/(-1-x^(2))=tan((2pi)/(3))` `rArr" "-(x^(3)+x)/(1+x^(2))tan(pi-(pi)/(3))` `rArr" "-(x^(3)-x)/(1+x^(2))=-tan.(pi)/(3)` `rArr" "(x(1+x^(2)))/(1+x^(2))=sqrt3.` `rArr" "x=sqrt3.` |
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