Find the value of other five trigonometric function `secx=(13)/5`, x lies in fourth quadrant.

Explanation

Given that `secx=13/5` and x lies in fourth quadrant.
`therefore secx=13/5` and x lies n fourth quadrant.
`therefore secx=13/5` and `cosx=1/(secx) rArr cosx=5/13`
`(therefore` x lies in fourth quadrant, therefore sec and cos ratio will be positive and remaining all ratio will be negative.)
`therefore sin^(2)x+cos^(2)=1`
`therefore sin^(2)x+(5/13)^(2)=1 rArr sin^(2)x=1-25/169 = 144/169`
`rArr sinx=-12/13`
`therefore "cosec"x=-1/(sinx)`
`rArr "cosec"x=1/(-12//13) = 1 xx (-13/12) = -13/12`
`therefore tanx=(sinx)/(cosx) = (-12//13)/(5//13) = -12/5`
`therefore cotx=1/(tanx) rArr cotx=1/(-12//5)`
`cotx=-5/12` Ans.
Therefore, `cosx=5/13, sinx=-12/13, "cosec "x=-13/12`,
`tanx=-12/5, cotx=-5/12` Ans.