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Question

If f(x)=cos(cot1(sin(tan1x))), then which of the following is(are) TRUE?

A
limxf(x)=12
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B
limxf(x)=12
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C
Range of f is (12,12)
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D
f(1)=13
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Solution

The correct option is D f(1)=13
limxf(x)=cos(cot1(sin(π2)))=12
limxf(x)=cos(cot1(sin(π2)))=12

Also, sin(tan1x)(1,1)
cot1(sin(tan1x))(π4,3π4)
cos(cot1(sin(tan1x))(12,12)
Range of f is (12,12)

f(1)=cos(cot1(sinπ4))
=cos(cot112)
=cos(tan12) (cot1x=tan11x, x>0)
=cos(cos113)
=13

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