find the exact value for cos(5pi/12)

Question

 Find the exact value of the question

 

Answer 1

let's write 5π/12 as the sum of two angles. 5π/12 = 2π/12 + 3π/12 = π/6 + π/4

 

Now, we have cos(π/6 + π/4) = cos(π/6) * cos(π/4) - sin(π/6) * sin(π/4)

 

= (√3/2)(√2/2) - (1/2)(√2/2)

 

= √6/4 - √2/4

 

= (√6 - √2)/4