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4(sin^4 30+cos^4 30) - 3(cos^2 45+sin^2 90)

Answer»

Step-by-step EXPLANATION:

4 ({ \sin}^{4} 30 + { \cos }^{4} 30) - 3( { \cos}^{2} 45 + { \sin }^{2} 90) \\ = > 4(( { \frac{1}{2} )}^{4} + { (\frac{ \sqrt{3} }{2} )}^{4} ) - 3 \: (( { \frac{1}{ \sqrt{2} } })^{2} + 1) \\ = > 4( \frac{1}{16} + \frac{9}{16} ) - 3( \frac{1}{2} + 1) \\ = > 4 \times \frac{10}{16} - 3( \frac{1 + 2}{2} ) \\ = > \frac{10}{4} - 3 \times \frac{3}{2} \\ = > \frac{10}{4} - \frac{9}{2} \\ = > \frac{10 - 18}{4} \\ = > \frac{ - 8}{4} \\ = > - 2


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