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`tan^(-1)""(x-1)/(x-2)+tan^(-1)""(x+1)/(x+2)=(pi)/(4)` <br> `implies tan^(-1)""((x-1)/(x-2)+(x+1)/(x+2))/(1-(x-1)/(x-2)*(x+1)/(x+2))=tan^(-1)1` <br> `((x-1)(x+2)+(x+1)(x-2))/((x-2)(x+2)-(x-1)(x+1))=1` <br> `implies (x^(2)+x-2+x^(2)-x-2)/((x^(2)-4)-(x^(2)-1))=1` <br> `implies (2x^(2)-4)/(-3)=1implies 2x^(2)-4= -3` <br> `implies 2x^(2)=1 implies x^(2)=(1)/(2)impliesx=pm(1)/(sqrt(2))`Transcript

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00:00 - 00:59 | hello kaisa welcome to daughter in today's question we are given if tan inverse of x minus one by X - 2 + 10 inverse of X + 1 by X + 2 is equal to pi by 4 now we have to find the value of x to be a given 10 inverse of x minus one by X - 2 + 10 inverse of X + 1 divided by X + 2 is equal to pi by 4 Sofia to find value of accessible use formula of tan inverse A + tan inverse of B which is tan inverse of a + b divided by 1 minus A into B here is x minus 1 divided by x minus 2 into X + 1 divided by X + 2 is equal to pi by 4 sunao 10 bill will go there schedule will come now here we will take LCM it will become x minus 2 into X + 2 here we get x minus one |

01:00 - 01:59 | X + 2 X + 1 x minus 2 is equal to 10 of fibre and denominator also we will take LCM schedule to come x minus 2 into X + 2 - of x minus 1 into X + 1 divided by x minus 2 and 2 X + 2 from these two terms will cancel each other out and we know that tan pi by 4 value is 1 from where we get x minus 1 into X + 2 clash of X + 1 into x minus 2 divided by x minus 2 and 2 X + 2 - of x minus 1 into X + 1 is equal to 1 chunavi Block Pune banquet set will become X square + of |

02:00 - 02:59 | two of x minus x minus of 2 year x minus 2 X + of x minus 2 / it will become a plus b minus b so it will become a square which is x square minus b square B square minus a x square minus 1 is equal to 1 from above we get to x square minus 4 upon here we will get x square - 4 + x square 9 plus minus x square + 1 is equal to 12 from here we get value as 2 x square minus 4 upon minus 3 is equal to 12 from where we get to x square minus 4 is equal to minus 3 so when we solve it we get to x square is equal to 1 and from where we get text valuation by route to show A |

03:00 - 03:59 | final value of x is 1 by root 2 thank you guys I hope you like my video |

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