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arc-tan-x-1-x-1-arc-tan-x-1-x-arc-tan-7-for-x-real-number-

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Question Number 106286 by bemath last updated on 04/Aug/20
arc tan (((x+1)/(x−1)))+arc tan (((x−1)/x))=arc tan (−7) for x real number
arctan(x+1x−1)+arctan(x−1x)=arctan(−7)forxrealnumber
Answered by bobhans last updated on 04/Aug/20
→arc tan (((x+1)/(x−1)))+arc tan (((x−1)/x))=arc tan (−7) tan (arc tan (((x+1)/(x−1)))+arc tan (((x−1)/x)))=tan (arc tan (−7)) ((((x+1)/(x−1))+((x−1)/x))/(1−((x+1)/(x−1)).((x−1)/x))) = −7⇒((x+1)/(x−1))+((x−1)/x)=−7(1−((x^2 −1)/(x^2 −x))) x^2 +x+x^2 −2x+1=−7(x^2 −x−x^2 +1) 2x^2 −x+1=−7(−x+1) 2x^2 −x+1=7x−7 ⇒2x^2 −8x+8=0 2(x−2)^2 = 0 ⇒x = 2. ★
→arctan(x+1x−1)+arctan(x−1x)=arctan(−7)tan(arctan(x+1x−1)+arctan(x−1x))=tan(arctan(−7))x+1x−1+x−1x1−x+1x−1.x−1x=−7⇒x+1x−1+x−1x=−7(1−x2−1x2−x)x2+x+x2−2x+1=−7(x2−x−x2+1)2x2−x+1=−7(−x+1)2x2−x+1=7x−7⇒2x2−8x+8=02(x−2)2=0⇒x=2.★
Answered by Dwaipayan Shikari last updated on 04/Aug/20
tan^(−1) (((x+1)/(x−1)))+tan^(−1) (((x−1)/x)) =tan^(−1) (((((x+1)/(x−1))+((x−1)/x))/(1−((x+1)/x))))=tan^(−1) ((((x^2 +x+x^2 −2x+1)/((x−1)x))/(−(1/x))))=tan^(−1) (−7) ⇒2x^2 −x+1=−7(1−x) ⇒2x^2 −8x−8=0 ⇒x^2 −4x+4=0⇒x=2
tan−1(x+1x−1)+tan−1(x−1x)=tan−1(x+1x−1+x−1x1−x+1x)=tan−1(x2+x+x2−2x+1(x−1)x−1x)=tan−1(−7)⇒2x2−x+1=−7(1−x)⇒2x2−8x−8=0⇒x2−4x+4=0⇒x=2

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