6cos30-3tg60+2sin45

Let's calculate the expression step by step, using the known values of the trigonometric functions: 1. **cos(30°)**: The value is \(\frac{\sqrt{3}}{2}\). 2. **tg(60°)**: The value is \(\sqrt{3}\). 3. **sin(45°)**: The value is \(\frac{\sqrt{2}}{2}\). Now plug these values into the expression: \[ 6 \cos(30°) - 3 \tan(60°) + 2 \sin(45° \] Substituting the values we have: \[ = 6 \left(\frac{\sqrt{3}}{2}\right) - 3\left(\sqrt{3}\right) + 2\left(\frac{\sqrt{2}}{2}\right) \] Now simplify each term: 1. \(6 \left(\frac{\sqrt{3}}{2}\right) = 3\sqrt{3}\) 2. \(-3(\sqrt{3}) = -3\sqrt{3}\) 3. \(2\left(\frac{\sqrt{2}}{2}\right) = \sqrt{2}\) Putting it all together: \[ = 3\sqrt{3} - 3\sqrt{3} + \sqrt{2} \] The \(3\sqrt{3}\) and \(-3\sqrt{3}\) cancel each other out: \[ = \sqrt{2} \] Thus, the final result is: \[ \sqrt{2} \]