Answer: cos(π/12) = (√2 + √6)/4
Step-by-step explanation:
The given function is
cos(π/12)
π/12 = 15 degrees
π/3 = 60 degrees
π/4 = 45 degrees
Thus, we can write
cos(π/12) = cos(π/3 - π/4)
We would apply the difference formula shown below
cos(a - b) = cosacosb + sinasinb
By comparing the formula with the given function,
a = π/3, b = π/4
By applying the formula, we have
cos(π/12) = cosπ/3cosπ/4 + sinπ/3sinπ/4
cosπ/3 = 1/2, cosπ/4 = √2/2
sinπ/3 = √3/2, sinπ/4 = √2/2
Thus,
cos(π/12) = 1/2 x √2/2 + √3/2 x √2/2
cos(π/12) = √2/4 + √6/4
cos(π/12) = (√2 + √6)/4