4. If `cos(x)=3/5`, solve `(1-sin(x))/cos(x)+cos(x)/(1-sin(x))`

Solution:
`cos(x)=3/5` (given)

`(1-sin(x))/cos(x)+cos(x)/(1-sin(x))=?`

`cos(x)=3/5`, in Quadrant-1

`(1)` `sin^2(x)=1-cos^2(x)`

`=1-(3/5)^2`

`=1-9/25`

`=(25-9)/25`

`=16/25`

`:.sin(x)=sqrt(16/25)=4/5=4/5`

`1-sin(x)=1/5`

`1-sin(x)`

`=1-(4/5)`

`=1+(-4)/5`

`=1/5`

Now substitute all these expression values in
`(1-sin(x))/(cos(x))+(cos(x))/(1-sin(x))`

`=(1/5)/(3/5)+(3/5)/(1/5)`

`=1/3+3`

`=10/3`

`:. (1-sin(x))/cos(x)+cos(x)/(1-sin(x))=10/3`

---

---