4sin²(60) - tan(45) / 3sin(45)
Using trigonometric identities:sin(60) = √3 / 2sin(45) = √2 / 2tan(45) = 1
Plugging in the values:4 ( √3 / 2)^2 - 1 / (3 √2 / 2)
Simplifying further:4 * 3/4 - 1 / (3√2/2)3 - 1 / (3√2/2)3 - 2 / 3√29√2 / 3√2 - 2 / 3√2(9 - 2) / 3√27 / 3√2
Therefore, the simplified expression is 7 / 3√2.
4sin²(60) - tan(45) / 3sin(45)
Using trigonometric identities:
sin(60) = √3 / 2
sin(45) = √2 / 2
tan(45) = 1
Plugging in the values:
4 ( √3 / 2)^2 - 1 / (3 √2 / 2)
Simplifying further:
4 * 3/4 - 1 / (3√2/2)
3 - 1 / (3√2/2)
3 - 2 / 3√2
9√2 / 3√2 - 2 / 3√2
(9 - 2) / 3√2
7 / 3√2
Therefore, the simplified expression is 7 / 3√2.