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Four compulsory topics in mathematics
Sin2a cos2a below refers to Sina's square and cosa's square. ...

Sinα-Cosα =-√ 5/2, because sin2a+cos2a= 1.

Then (sinα-cosα) 2 = sin2a+cos2a-2sina * COSA = 5/4.

So SINA * COSA =- 1/8, then tan α+cot α = Sina/COSA+COSA/SINA = (SIN2A+COS2A)/COSA * SINA =1/COSA * SINA =-8.

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