How do you use the half-angle identity to find the exact value of cos(-pi/12)? Trigonometry Trigonometric Identities and Equations Half-Angle Identities 1 Answer Dharma R. Sep 22, 2015 #sqrt(2+sqrt3)/2# Explanation: #cos(-pi/12)=cos(pi/12)##as# #cos(x)# #is# #a# #even function# # f(x)=f(-x)# #costheta=sqrt((1+cos2theta)/2)# #=>cos(pi/12)=sqrt((1+cos(pi/6))/2)=sqrt((1+sqrt3/2)/2)=sqrt(2+sqrt3)/2# Answer link Related questions What is the Half-Angle Identities? How do you use the half angle identity to find cos 105? How do you use the half angle identity to find cos 15? How do you use the half angle identity to find sin 105? How do you use the half angle identity to find #tan (pi/8)#? How do you use half angle identities to solve equations? How do you solve #\sin^2 \theta = 2 \sin^2 \frac{\theta}{2} # over the interval #[0,2pi]#? How do you find the exact value for #sin105# using the half‐angle identity? How do you find the exact value for #cos165# using the half‐angle identity? How do you find the exact value of #cos15#using the half-angle identity? See all questions in Half-Angle Identities Impact of this question 2760 views around the world You can reuse this answer Creative Commons License