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cot-1(sqrt(1+x2)-x) please give me solution...........................

cot-1(sqrt(1+x2)-x) please give me solution...........................

Grade:12

2 Answers

Arun
25750 Points
6 years ago
Dear Manisha
put x = cot@
now 
sqrt (1 + x^2) = cosec@
now 
cot^-1 [cosec@ – cot@]
cot^-1 [(1 – cos@)/ sin@]
cot^-1 [(2 sin^2 @/2 ) / 2 sin@/2 * cos@/2]
cot^-1 [tan@/2]
cot^-1 [cot(pi/2 – @/2)]
\pi / 2 – ½ cot-1x
Regards
Arun (askIITians forum expert)
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

put x = cot@
now
sqrt (1 + x^2) = cosec@
now
cot^-1 [cosec@ – cot@]
cot^-1 [(1 – cos@)/ sin@]
cot^-1 [(2 sin^2 @/2 ) / 2 sin@/2 * cos@/2]
cot^-1 [tan@/2]
cot^-1 [cot(pi/2 – @/2)]
pi/2 – ½ cot-1x

Thanks and Regards

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