3. If `tan(x)=1/2`, solve `(1-tan^2(x))/(1+tan^2(x))+(2tan(x))/(1+tan^2(x))`

Solution:
`tan(x)=1/2` (given)

`(1-tan^2(x))/(1+tan^2(x))+(2tan(x))/(1+tan^2(x))=?`

`tan(x)=1/2`, in Quadrant-1

`1-tan^2(x)=3/4`

`1-tan^2(x)`

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

`=1+(-1)/4`

`=3/4`

`1+tan^2(x)=5/4`

`1+tan^2(x)`

`=1+(1/2)^2`

`=1+1/4`

`=5/4`

`2tan(x)=1`

`2tan(x)`

`=2*(1/2)`

`=1`

Now substitute all these expression values in
`(1-tan^2(x))/(1+tan^2(x))+(2tan(x))/(1+tan^2(x))`

`=(3/4)/(5/4)+(1)/(5/4)`

`=3/5+4/5`

`=7/5`

`:. (1-tan^2(x))/(1+tan^2(x))+(2tan(x))/(1+tan^2(x))=7/5`

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