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solve for x sin[cot^-1(x+1)]=cos[tan^-1(x)] when i write cot inverse x as pi by 2 – tan inverse x. x gets cancelled

solve for x
sin[cot^-1(x+1)]=cos[tan^-1(x)]
when i write cot inverse x as pi by 2 – tan inverse x. x gets cancelled

Grade:12

1 Answers

Chandrasekar Ram J
11 Points
3 years ago
cot^-1(x+1) = sin^-1(1/sqrt(1+(1+x)²)
tan^-1(x) = cos^-1(1/sqrt(x²+1))
hence,  sin(cot^-1(x+1))    = cos(tan^-1(x))
             sin(sin^-1(1/sqrt(1+(1+x)²))=cos(cos^-1(1/sqrt(x²+1)))
             1/sqrt(1+(1+x)²=1/sqrt(x²+1)
      ==> 1+(1+x)² = x² + 1
     ==> 1 + 1 + x² + 2x = x² + 1
     ==>  2x = -1
    ==> x = – 1/2

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