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Question:

A value of x satisfying the equation sin[cot(1+x)]=cos[tanx], is.

12

π

0

π/2

Solution:

From first figure,sin(cot(1+x))=1/√(1+(1+x)²+2x)=1/√(x²+2x+2)
From second figure,cos(tanx)=1/√(1+x²)
sin(cot(1+x))=cos(tan(x)) → x²+2x+2=1+x² → 2x=-1 → x=-1/2