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Evaluate Cos 45o Cos 30o - Sin 45o Sin 30o leaving the answer in surd form...


Question

Evaluate Cos 45o Cos 30o - Sin 45o Sin 30o leaving the answer in surd form

Options

A) \(\frac{\sqrt{2}-1}{2}\)

B) \(\frac{\sqrt{3}-\sqrt{2}}{4}\)

C) \(\frac{\sqrt{6}-\sqrt{2}}{2}\)

D) \(\frac{\sqrt{6}-\sqrt{2}}{4}\)

The correct answer is D.

Explanation:

\(cos45^o \times cos30^o - sin45^o \times sin30^o\\\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2} - \frac{1}{\sqrt{2}}\times \frac{1}{2}\\\frac{\sqrt{3}}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}; = \frac{\sqrt{3}-1}{2\sqrt{2}}=\frac{\sqrt{6}-\sqrt{2}}{4}\)

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Dicussion (1)

  • \(cos45^o \times cos30^o - sin45^o \times sin30^o\\\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2} - \frac{1}{\sqrt{2}}\times \frac{1}{2}\\\frac{\sqrt{3}}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}; = \frac{\sqrt{3}-1}{2\sqrt{2}}=\frac{\sqrt{6}-\sqrt{2}}{4}\)

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