Please help?

enter image source here

1 Answer
Mar 20, 2018

color(red)(sin(A+B)=171/221, cos(A+B)=140/221, tan (A+B)=171/140

Explanation:

You have sin B=8/17 and cosA=12/13.

From this information, compute cosB and sin A

sinA=sqrt(1-cos^2A)=5/13

cos B=sqrt(1-sin^2B)=15/17

So, tanA=sinA/cosA=5/12 and

tanB=sinB/cosB=8/15

color(blue) sin(A+B) color(blue)= color(blue)(sinAcosB+cosAsinB
color(blue)(=5/13*15/17+12/13*8/17= 171/221

color(green)(cos(A+B)=sinAsinB-cosAcosB
color(green)(=12/13*15/17-5/13*8/17=140/221

color(brown)(tan(A+B)=(tanA+tanB)/(1-tanAtanB)
color(brown)(=(5/12+8/15)/(1-5/12*8/15)=171/180*9/7=171/140