If sin(cot-'(x + 1) = cos(tan-' x),...
Question
Fullscreen

If sin(cot-'(x + 1) = cos(tan-' x), then x = (c) O (d)

JEE/Engineering Exams
Maths
Solution
53
Rating
4.0 (1 ratings)
Fullscreen
Given that ( sin left[cot ^{-1}(x+1)right]=cos left(tan ^{-1} xright) ldots(1) ) We know that, ( cot ^{-1} A=sin ^{-1} frac{1}{sqrt{1+A^{2}}} ) Here, ( A=x+1 ) Applying this identity in equation ( (1), ) we have, ( sin left[sin ^{-1} frac{1}{sqrt{1+(1+x)^{2}}}right]=cos left(tan ^{-1} xright) ldots .(2) ) A/so we know that, ( tan ^{-1} A=cos ^{-1} frac{1}{sqrt{1+A^{2}}} ) Here, ( A=x ) Applying this identity in equation ( (2), ) we have, ( sin left[sin ^{-1} frac{1}{sqrt{1+(1+x)^{2}}}right]=cos left(cos ^{-1} frac{1}{sqrt{1+x^{2}}}right) ) ( Rightarrow frac{1}{sqrt{1+(1+x)^{2}}}=frac{1}{sqrt{1+x^{2}}} ) Squaring and reciprocating both the sides, we have, ( 1+(1+x)^{2}=1+x^{2} ) ( Rightarrow 1+1+x^{2}+2 x=1+x^{2} ) ( Rightarrow 1+2 x=0 ) ( Rightarrow x=frac{-1}{2} )
Quick and Stepwise Solutions Just click and Send Download App OVER 20 LAKH QUESTIONS ANSWERED Download App for Free