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prove that cot{tan^-1x + tan^1 1+x}+ cos(1-2x^2)+cos^-1(2x^2-1)=pi

prove that cot{tan^-1x + tan^1 1+x}+ cos(1-2x^2)+cos^-1(2x^2-1)=pi

Grade:12

1 Answers

Arun
25750 Points
6 years ago

Dear student

 

cot (tan^-1 x + cot^-1 x) + cos ^-1 (- (2 x^2 – 1)) + cos ^-1 (2 x^2 – 1)

 = cot (\pi/2) + \pi – cos ^-1 (- (2 x^2 – 1)) + cos ^-1 (2 x^2 – 1)

 = 0 + \pi – 0

 = \pi

Hence proved

 

Regards

Arun (askIITians forum expert)

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