Question

Please help?

Answer 1

`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`