Suppose sin alpha 13 with alpha is Quodrant I and cos beta

Suppose sin alpha = 1/3, with alpha is Quodrant I, and cos beta = -1/4, with beta in Quodrant II Find the exact value of each of the following. sin (alpha + beta) cos(alpha - beta)

Solution

sin =1/3 =>cos =((3²-1²))/3 =(8)/3

cos =-1/4=>sin=((4²-1²))/4=(15)/4

20)sin(+)=sincos+cossin

sin(+)=(1/3)(-1/4) +((8)/3)((15)/4)

sin(+)=(-1/12) +((120)/12)

sin(+)=((120) -1)/12

21)cos(-)=cos()cos() +Sin()sin()

cos(-)=((8)/3)(-1/4) +(1/3)((15)/4)

cos(-)=((-8)/12) +((15)/12)

cos(-)=(15-8)/12