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Question

The value of 4x for which sin[cot1(1+x)]=cos(tan1x) is _______.

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Solution

sin[cot1(1+x)]=sin(π2tan1x)[cot1(1+x)]=(π2tan1x)tan11(1+x)=π2tan1xtan1⎢ ⎢ ⎢11+x+x1x(1+x)⎥ ⎥ ⎥=π2x2+x+1(1+x)1(1+x)=tanπ2x2+x+1=itsrootsisx=(1+3)2orx=(31)2therefore4x=4×(1+3)2

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