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Find the value of tan² 45° − tan² 60°.

Find the value of tangent squared 45 degrees minus tangent squared of 60 degrees.

Tangent squared 45 is the value of tangent 45 squared. The same thing is true for the tangent squared of 60 degrees. We need the tangent of 60 degrees squared. We want the difference between these two angles’ square.

I know that the tangent of 45 degrees is one, one squared. The tangent of 60 degrees equals the square root of three squared. And we want the difference. One squared equals one minus the square root of three squared equals three and one minus three equals negative two.

Tangent 45 squared minus tangent of 60 squared equals negative two.

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