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Question

# Which of the following pairs of function/functions has same graph?

A
y=tan(cos1x);y=1x2x
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B
y=tan(cot1x);y=1x
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C
y=sin(tan1x);y=x1+x2
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D
y=cos(tan1x);y=sin(cot1x)
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Solution

## The correct options are A y=tan(cos−1x);y=√1−x2x B y=tan(cot−1x);y=1x C y=sin(tan−1x);y=x√1+x2 D y=cos(tan−1x);y=sin(cot−1x)y=tan(cos−1x);y=√1−x2x Domain of the functions D1=[−1,1]−{0}D2=[−1,1]−{0} Now, we know that, y=tan(cos−1x)⇒y=tan(tan−1√1−x2x)⇒y=√1−x2x Therefore the function indentical, hence they will have same graph. y=tan(cot−1x);y=1x D1=R−{0}D2=R−{0} We know that, y=tan(cot−1x)⇒y=tan(tan−11x)=1x Therefore the function indentical, hence they will have same graph. y=sin(tan−1x);y=x√1+x2 Domain of both the function is R and y=sin(tan−1x)⇒y=sin(sin−1x√1+x2)⇒y=x√1+x2 Therefore the function indentical, hence they will have same graph. y=cos(tan−1x);y=sin(cot−1x) Domain of both the function is R and y=cos(tan−1x)⇒y=cos(cos−11√1+x2)⇒y=1√1+x2 y=sin(cot−1x)⇒y=sin(1√1+x2)⇒y=1√1+x2 Therefore the function indentical, hence they will have same graph.

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