Question

Find the exact value of cos 15°

Answer 1

Answer:

$\frac{\sqrt{6}+\sqrt{2} }{4}$

Step-by-step explanation:

Using the difference formula for cosine and the exact values

cos45° = sin45° = $\frac{\sqrt{2} }{2}$, cos30° = $\frac{\sqrt{3} }{2}$, sin30° = $\frac{1}{2}$

cos(a - b) = cosacosb + sinasinb

Note 15° = 45° - 30°, thus

cos15°

= cos(45 - 30)°

= cos45°cos30° + sin45°sin30°

= ($\frac{\sqrt{2} }{2}$ × $\frac{\sqrt{3} }{2}$ ) + ($\frac{\sqrt{2} }{2}$ × $\frac{1}{2}$ )

= $\frac{\sqrt{6} }{4}$ + $\frac{\sqrt{2} }{4}$

= $\frac{\sqrt{6}+\sqrt{2} }{4}$

Answer 2

Answer:

$\frac{\sqrt{6} +\sqrt{2} }{4}$

Step-by-step explanation: