Home > Calculus > Trigonometry > If sin(x)=1/2, then solve trigonometric expression cos(x)csc(x) example

2. If sin(x)=1/2, then solve trigonometric expression cos(x)csc(x) example ( Enter your problem )
  1. If `sin(x)=3/5`, solve `cos(x)csc(x)+tan(x)sec(x)`
  2. If `cos(x)=3/5`, solve `(1-sin(x))/cos(x)+cos(x)/(1-sin(x))`
  3. If `tan(x)=1/2`, solve `(1-tan^2(x))/(1+tan^2(x))+(2tan(x))/(1+tan^2(x))`
  4. If `cos(x)=3/5`, solve `(1-sin(x))/cos(x)+cos(x)/(1-sin(x))`

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





2. 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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