use a sum or difference identity to find an exact value
pie/12
cos pie/12
Hmmm. 15 degrees. I know 45, and 30, so why not the difference?
Cos15=cos(45-30) = you know the formula
i got it nevermind
To find the exact value of π/12 using a sum or difference identity, we can use the formula for the half-angle identity for the tangent function.
The half-angle identity for the tangent function is given by:
tan^2(x/2) = (1 - cos(x)) / (1 + cos(x))
Rearranging this equation, we have:
tan(x/2) = √((1 - cos(x)) / (1 + cos(x)))
Now, we need to find the value of cos(π/6) in order to substitute it into the formula. We know that cos(π/6) = √3/2.
Substituting cos(π/6) = √3/2 into the formula, we get:
tan(π/12) = √((1 - (√3/2)) / (1 + (√3/2)))
To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator:
tan(π/12) = √((1 - (√3/2)) / (1 + (√3/2))) * (√3 - 2) / (√3 - 2)
Simplifying further, we get:
tan(π/12) = (√(√3 - 1))/(√3 + 1)
Therefore, the exact value of π/12 using a sum or difference identity is (√(√3 - 1))/(√3 + 1).