Cos(pi/3 + b) = see picture! explain !

Hello from MrBillDoesMath!

 cos (pi/3 + B)  =   1/2( cosB - sqrt(3) sinB)

 the first item in the list.

Discussion:

The standard double-angle formula for cos is:

cos (A + B) = cosAcosB - sinAsinB

Applying this formula to cos (pi/3 + B ) gives

cos(pi/3 + B) = cos(pi/3)cosB - sin(pi/3)sinB

But cos(pi/3) = cos (180/3) = cos(60) = 1/2 and

      sin(pi/3) =  sqrt(3)/2

Substituting these values gives

cos (pi/3 + B) =  1/2 cosB - sqrt(3)/2 sinB =

                          1/2( cosB - sqrt(3) sinB)

which is the first answer.

Regards,  

MrB

answer: i feel you honey.

step-by-step explanation: