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Question: The value of \(\cos 15{^\circ} - \sin 15{^\circ}\)is equal to...

The value of cos⁡15∘−sin⁡15∘\cos 15{^\circ} - \sin 15{^\circ}is equal to

A

12\frac{1}{\sqrt{2}}

B

12\frac{1}{2}

C

−12- \frac{1}{\sqrt{2}}

D

0

Answer

12\frac{1}{\sqrt{2}}

Explanation

Solution

cos⁡15o−sin⁡15o=2.cos⁡(45o+15o)=2.cos⁡60o\cos 15^{o} - \sin 15^{o} = \sqrt{2}.\cos(45^{o} + 15^{o}) = \sqrt{2}.\cos{}60^{o}

=2.12=12= \sqrt{2}.\frac{1}{2} = \frac{1}{\sqrt{2}}.