# Write cos{(pi-:4)-a} in terms of trigonometric ratios of just a?

Oct 2, 2017

$\cos \left\{\left(\pi \div 4\right) - a\right\} = \frac{1}{\sqrt{2}} \left(\cos a + \sin a\right)$

#### Explanation:

As $C o s \left(A - B\right) = \cos A \cos B + \sin A \sin B$

$\cos \left\{\left(\pi \div 4\right) - a\right\} = \cos \left(\frac{\pi}{4} - a\right)$

= $\cos \left(\frac{\pi}{4}\right) \cos a + \sin \left(\frac{\pi}{4}\right) \sin a$

= $\frac{1}{\sqrt{2}} \cos a + \frac{1}{\sqrt{2}} \sin a$

= $\frac{1}{\sqrt{2}} \left(\cos a + \sin a\right)$