Question

(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Answer 1

Given that

`\begin{gathered} \cos A=(8)/(17)\text{ and } \\ \sin B=(5)/(13) \end{gathered}`

Let's draw the two diagrams for angles A and B

Hence,

`\begin{gathered} \sin A=(15)/(17) \\ \cos B=(12)/(13) \\ \tan A=(15)/(8) \\ \tan B=(5)/(12) \end{gathered}`

Therefore,

`\sin (A+B)=\sin A\cos B+\sin B\cos A=(15)/(17)*(12)/(13)+(5)/(13)*(8)/(17)=(220)/(221)`
`\sin (A-B)=\sin A\cos B-\sin B\cos A=(15)/(17)*(12)/(13)-(5)/(13)*(8)/(17)=(140)/(221)`
`\tan (A+B)=(\tan A+\tan B)/(1-\tan A\tan B)=((15)/(8)+(5)/(12))/(1-(15)/(8)*(5)/(12))=(220)/(21)`
`\tan (A-B)=(\tan A-\tan B)/(1+\tan A\tan B)=((15)/(8)-(5)/(12))/(1+(15)/(8)*(5)/(12))=(140)/(171)`