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Question

Ifsin[cot1(x+1)]=cos(tan1x), then find x

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Solution

sin[cot1(x+1)]=cos(π2cot1(x+1))=cos(tan1(x))
if cosx=cosθ
then x=2nπ+θ,x=2nπθ
π2cot1(x+1)=2nπ+tan1(x)
apply tan on both sides
cot(cot1(x+1))=tan(2nπ+tan1(x))
x+1=x
x does not exist
now consider another case
x=2nπθ
π2cot1(x+1)=2nπtan1(x)
apply tan on both sides
cot(cot1(x+1))=tan(2nπtan1(x))
x+1=x
x=12

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