What is the value of cos (15°) + cos (105°) ?

⇒ cos (15°) + cos (105°)

= 2cos (\(\frac{120}{2}\)) cos (\(\frac{90}{2}\))

( because cos A + cos B = 2 cos (\(\frac{A+B}{2}\)) cos (\(\frac{A-B}{2}\))

= 2cos 60° cos 45°

= 2 × \(\frac{1}{2}\) × \(\frac{1}{\sqrt {2 }}\)

= \(\frac{1}{\sqrt {2 }}\)