The value of x which satisfies sin ⁡ ( cot^-1 ⁡x )= cos ⁡( tan^-1 ⁡ (1+x )) is

Question

Accepted Answer

Correct answer: A. (a) We have, sin ( cot^-1x )= cos ( tan^-1(1+x) ) … . (i ) And we know that cot^-1 ⁡x= sin^-1 ⁡ ( 1 1+x^2 ) and tan^-1 ⁡x= cos^-1 ⁡ ( 1 1+x^2 ) ∴ From Eq. (i) we get sin ⁡ ( sin^-1 ⁡ 1 1+x^2 )= cos ⁡ ( cos^-1 ⁡ 1 1+ (1+x )^2 ) 1 1+x^2= 1 1+ (1+x )^2 1+ (1+x )^2= 1+x^2 On squaring both the sides, we get 1+x^2+2x+1=x^2+1 ∴x=- 12.

$The value of x which satisfies sin (cot^{- 1} x) = cos (tan^{- 1} (1 + x)) is$

Solution

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