Question

cos 15° - sin 15°
cos 15° + sin 15°​

Answer 1

Answer:

0.9747

Hi !!

cos 15 degree - sin 15 degree

cos 15 degree + sin 15 degree

= 0.9747

Answer 2

What do we have :

$sin 15^o=\frac{\sqrt{3}-1 }{2\sqrt{2} }$

$cos 15^o=\frac{\sqrt{3}+1 }{2\sqrt{2} }$

Simplification :

a) $cos 15^o- sin 15^o$

 $=\frac{\sqrt{3}+1 }{2\sqrt{2} }-\frac{\sqrt{3}-1 }{2\sqrt{2} }$

$= \frac{2}{2\sqrt{2} }=\frac{1}{\sqrt{2} }$

b) $cos 15^o + sin 15^o$

$=\frac{\sqrt{3}+1 }{2\sqrt{2} }+\frac{\sqrt{3}-1 }{2\sqrt{2} }$

$=\frac{2\sqrt{3} }{2\sqrt{2} } =\sqrt{\frac{3}{2} }$