How do you find the exact value of #cos(pi/4+pi/3)#? Trigonometry Trigonometric Identities and Equations Sum and Difference Identities 1 Answer Monzur R. Sep 23, 2017 #cos(pi/4+pi/3) = (sqrt2-sqrt6)/4# Explanation: In order to evaluate #cos(pi/4+pi/3)# we need to use the compound angle formula for cos: #cos(A+B) -= cosAcosB-sinAsinB# #therefore cos(pi/4+pi/3) = cos(pi/4)cos(pi/3)-sin(pi/4)sin(pi/3) = 1/sqrt2 *1/2 - 1/sqrt2*sqrt3/2 = 1/(2sqrt2)-sqrt3/(2sqrt2) = (1-sqrt3)/(2sqrt2)=(sqrt2-sqrt6)/4# Answer link Related questions What are some sum and difference identities examples? How do you use the sum and difference identities to find the exact value of #cos 15^@#? How do you use the sum and difference identities to find the exact value of cos 75? How do you use the sum and difference identities to find the exact value of tan 105 degrees? How do you apply the sum and difference formula to solve trigonometric equations? How do you evaluate #sin(45)cos(15)+cos(45)sin(15)#? How do you write #cos75cos35+sin75sin 35# as a single trigonometric function? How do you prove that #cos(x-y) = cosxcosy + sinxsiny#? How do you evaluate #cos((3pi)/5)cos((4pi)/15)+sin((3pi)/5)sin((4pi)/15)#? If sinA=4/5 and cosB= -5/13, where A belongs to QI and B belongs to QIII, then find sin(A+B).... See all questions in Sum and Difference Identities Impact of this question 12042 views around the world You can reuse this answer Creative Commons License