Question

find value of cos π/24​

Answer 1

Answer:

√[(4+√6+√2)/8]

Step-by-step explanation:

π/24 = 7.5°

 

First, find cos15° using the fact that 15° = 45° - 30°. then use a half angle identity to find cos7.5°.

 

cos15° = cos(45° - 30°)

 

          = cos45°cos30° + sin45°sin30° = (√2/2)(√3/2) + (√2/2)(1/2) = (√6+√2)/4

 

So, cos(π/24) = cos(7.5°) = √[(1+cos15°)/2]  

 

                                      = √[(1+(√6+√2)/4)/2] = √[(4+√6+√2)/8]