Question

How do you find the value of `cos ((13pi)/12)`?

Answer 1

`=-1/2sqrt(1/2(sqrt3+1))`

Explanation:

`cos((13pi)/12)=cos(pi+pi/12)=-cos((pi)/12)`
`=-sqrt(1/2(1+cos(2*pi/12)))=-sqrt(1/2(1+cos(pi/6)))`
`=-sqrt(1/2(1+sqrt3/2))=-sqrt(1/8(4+2*sqrt3))`
`=-sqrt(1/(2*2^2)((sqrt3)^2+2*sqrt3*1+1^2))`
`=-sqrt(1/(2*2^2)(sqrt3+1)^2)`

`=-1/2sqrt(1/2(sqrt3+1))`