solve: tanx+cotx=1, xE[0,2pi]

Solve using teh trig identies.
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sinx/cosx+cosx/sinx=(sin^2x+cos^2x)/sinxcosx=1/(sinxcosx)=2/(2sinxcosx)=2/sin2x=1, so sin2x=2. But sine cannot be greater than 1, so there is no solution. The minimum value of the expression is 2, when 2x=90, x=45 degrees ((pi)4) i.e., sin2x=1.

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