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Which of the following pairs of function/functions has same graph?`y=tan(cos^(-1)x); y=(sqrt(1-x^2))/x``y=t a n(cot^(-1)x);y=1/x``y="sin"(tan^(-1)x); y=x/(sqrt(1-x^2))``y="cos"(tan^(-1)x); y=s in(cot^(-1)x)` |
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Answer» (i) `y = tan(cos^-1x) and y = sqrt(1-x^2)/x` `=>y = tan(tan^-1(sqrt(1-x^2)/x)) and y = sqrt(1-x^2)/x` `=>y = sqrt(1-x^2)/x and y = sqrt(1-x^2)/x` `:.` Domain and range of both functions are same, so there graphs will be same. (ii) `y = tan(cot^-1x) and y = 1/x` `=>y = tan(tan^-1(1/x)) and y = 1/x` `=>y = 1/x and y = 1/x` `:.` Domain and range of both functions are same, so there graphs will be same. (iii) `y = sin (tan^-1x) and y = x/sqrt(1-x^2)` `=>y = sin(sin^-1( x/sqrt(1-x^2))) and y = x/sqrt(1-x^2)` `=>y = x/sqrt(1-x^2) and y = x/sqrt(1-x^2)` `:.` Domain and range of both functions are same, so there graphs will be same. (iv) `y = cos (tan^-1x) and y = sin(cot^-1x)` `=>y = cos(cos^-1(1/(sqrt(1+x^2)))) and y = sin(sin^-1(1/(sqrt(1+x^2))))` `=> y = 1/(sqrt(1+x^2)) and y = 1/(sqrt(1+x^2))` `:.` Domain and range of both functions are same, so there graphs will be same. |
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