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