Evaluate : `4(sin^4 30^0+cos^4 60^0)-2/3(sin^2 60^0-cos^2 45^0)+1/2tan^2 60^0`

Explanation

Given: ` 4(sin ^4 30^circ+cos ^4 60^circ)-frac{2}{3}(sin ^2 60^circ-cos ^2 45^circ)+frac{1}{2} tan ^2 60^circ`


`=4(frac{1}{2})^{4}+(frac{1}{2})^{4}-frac{2}{3}((frac{sqrt{3}}{2})^{2}-(frac{1}{sqrt{2}})^{2})+frac{1}{2}(sqrt{3})^{2}`


`=4((frac{1}{16})+(frac{1}{16}))-frac{2}{3}((frac{3}{4})-(frac{1}{2}))+frac{3}{2}`


`=4(frac{2}{16})-frac{2}{3}(frac{1}{4})+frac{3}{2}`


`=frac{1}{2}-frac{1}{6}+frac{3}{2}`


`=frac{4}{2}-frac{1}{6}`


`=frac{2}{1}-frac{1}{6} `


`=2-frac{1}{6}`


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