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`
This material is intended as a summary. Use your textbook for detail explanation.
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