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Question

If the mapping f(x)=ax+b,a>0 maps [āˆ’1,1] onto [0,2] then cot[cotāˆ’17+cotāˆ’18+cotāˆ’118] is equal to

A
f(1)
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B
f(0)
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C
f(1)1
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D
f(1)+1
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Solution

The correct option is D f(1)+1
f(1)=0a+b=0f(1)=2a+b=2b=1,a=1f(x)=x+1cot[tan117+tan118+tan1118]=cot[tan1(1555)+tan1(118)]=cot[tan1(65195)]=cot[tan1(13)]=3=f(1)+1

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