Evaluate Cos 45
o Cos 30
o - Sin 45
o Sin 30
o leaving the answer in surd form
A. \(\frac{\sqrt{2}-1}{2}\)
B. \(\frac{\sqrt{3}-\sqrt{2}}{4}\)
C. \(\frac{\sqrt{6}-\sqrt{2}}{2}\)
D. \(\frac{\sqrt{6}-\sqrt{2}}{4}\)
Correct Answer: D
Explanation
\(cos45^o \times cos30^o - sin45^o \times sin30^o\\
\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2} - \frac{1}{\sqrt{2}}\times \frac{1}{2}\\
\frac{\sqrt{3}}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}; = \frac{\sqrt{3}-1}{2\sqrt{2}}=\frac{\sqrt{6}-\sqrt{2}}{4}\)
