Q. 12 - Precalculus Enhanced with Graphing Utilities

Question

find the exact value of the expression  

$2{\sin }^{2}60°-3\cos 45°$

Step-by-Step Solution

Answer

$2{\sin }^{2}60°-3\cos 45°=3\left(\frac{1}{2}-\frac{1}{\sqrt{2}}\right)$

Step 1. Rewriting the expression

Given expression can be written as$2{(\sin 60°)}^2-\cos 45°$

Step 2. Calculations

$$\begin{gathered} \sin 60°=\frac{\sqrt{3}}{2} \\ \cos 45°=\frac{1}{\sqrt{2}} \\ So 2{(\sin 60°)}^2-3\cos 45°=2{\left(\frac{\sqrt{3}}{2}\right)}^2-\frac{3}{\sqrt{2}}=\frac{3}{2}-\frac{3}{\sqrt{2}} \\ = 3\left(\frac{1}{2}-\frac{1}{\sqrt{2}}\right) \end{gathered}$$