Grade 12Trigonometry

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

manisha grang

8 Years agoGrade 12

2 Answers

Arun

8 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

6 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