Evaluate Cos 45o Cos 30o - Sin 45o Sin 30o 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
\(\frac{\sqrt{6}-\sqrt{2}}{4}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(cos45^o \times cos30^o - sin45^o \times sin30^o\)
\(\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2} - \frac{1}{\sqrt{2}}\times \frac{1}{2}\)
\(\frac{\sqrt{3}}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}; = \frac{\sqrt{3}-1}{2\sqrt{2}} = \frac{\sqrt{6}-\sqrt{2}}{4}\)
Source: Myschool Past Questions Archive (Record #26610)