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Find If sin(x)=5/13 then find cos(x)csc(x)+tan(x)sec(x)

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Your problem `->` If sin(x)=5/13 then find cos(x)csc(x)+tan(x)sec(x)


`sin(x)=5/13` (given)

`cos(x)csc(x)+tan(x)sec(x)=?`

`sin(x)=5/13`

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

`=1-(5/13)^2`

`=1-25/169`

`=(169-25)/169`

`=144/169`

`:.cos(x)=sqrt(144/169)=12/13`


`(2)` `tan(x)=sin(x)/cos(x)=(5/13)/(12/13)=5/12`


`(3)` `csc(x)=1/sin(x)=1/(5/13)=13/5`


`(4)` `sec(x)=1/cos(x)=1/(12/13)=13/12`


Now substitute all these expression values in
`cos(x)csc(x)+tan(x)sec(x)`

`=(12/13)*(13/5)+(5/12)*(13/12)`

`=12/5+65/144`

`=2053/720`

`:. cos(x)csc(x)+tan(x)sec(x)=2053/720`






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