use a sum or difference identity to determine a value of x b

use a sum or difference identity to determine a value of x between 0 and 360 that makes the statement true. sin(x)=sin(329)cos(148)-cos(329)sin(148)

Solution

sin(x)=sin(329)cos(148)-cos(329)sin(148)

As there is -ve sign between the two terms we would use difference formula for sine:

sin(A-B) = sinAcosB - sinBcosA

sin(x)=sin(329)cos(148)-cos(329)sin(148)

= sin(329 -148) = sin(181)

x = 181