Evaluate the following: 2 tan2 45° cos230° sin260°.

Solution:

[latex]2tan^{2}45^{\circ}+cos^{2}30^{\circ}-Sin^{2}60^{\circ}[/latex]

Rewriting the above equation, we get:

[latex]2(tan45^{2}+cos30^{2}-Sin60^{2})[/latex]

Simplifying further, we get

[latex]2(1)+(\frac{\sqrt{3}}{2})^2-(\frac{\sqrt{3}}{2})^2=2[/latex]

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