Question

I need help with 6, 7, and 8.

Answer 1

`cos\ u=-(15)/(15)\implies sin\ u=(√(210))/(15)\\\\sin\ v=-(5)/(13)\implies cos\ v=-(12)/(13)`

6.Answer:
`\bold{(12√(15)+5√(210))/(195)}`

Explanation:

`cos(u+v)=cosu\cdot cosv-sinu\cdot sinv\\\\.\qquad\qquad=(-√(15))/(15)\cdot (-12)/(13)-(√(210))/(15)\cdot (-5)/(13)\\\\\\.\qquad\qquad=(12√(15))/(195)+(5√(210))/(195)\\\\\\.\qquad\qquad=\boxed{(12√(15)+5√(210))/(195)}`

7.
`\bold{(-12√(210)-5√(15))/(195)}`

Explanation:

`sin(u-v)=sinu\cdot cosv-cosu\cdot sinv\\\\.\qquad\qquad=(√(210))/(15)\cdot (-12)/(13)-(-√(15))/(15)\cdot (-5)/(13)\\\\\\.\qquad\qquad=(-12√(210))/(195)-(5√(15))/(195)\\\\\\.\qquad\qquad=\boxed{(-12√(210)-5√(15))/(195)}`

8.Answer:
`\bold{-(19)/(67)}`

Explanation:

`tan\ u=-(3)/(4)\\\\cos\ v=-(12)/(13)\implies tan\ v=(5)/(13)\\\\\\\\tan(u+v)=(tan\ u+tan\ v)/(1-tan\ u\cdot tan\ v)\\\\\\.\qquad\qquad=((-3)/(4)+(5)/(13))/(1-((-3)/(4)\cdot (5)/(13)))\\\\\\.\qquad\qquad=((-39)/(52)+(20)/(52))/((52)/(52)+(15)/(52))\\\\\\.\qquad\qquad=\boxed{-(19)/(67)}`