If `sec theta=13/12`, find the values of other trigonometric ratios.

Explanation

Consider `DeltaABC` where

`/_ABC=90^(@),/_ACB=theta`
`sec theta=(AC)/(BC)`
`sec theta=13/12`
`:.(AC)/(BC)=13/12`
`:.AC=13k` and `BC=12k`
In right angled `DeltaABC`
By Pythagoras theorem,
`AC^(2)=AB^(2)+BC^(2)`
`:.(13k)^(2)=AB^(2)+(12k)^(2)`
`:.AB^(2)=169k^(2)-144k^(2)`
`:.AB^(2)=25k^(2)`
`:.AB=5k` ..(Taking square roots of both the sides)
`sin theta=(AB)/(AC)=(5k)/(13k)=5/13`
`cos theta=(BC)/(AC)=(12k)/(13k)=12/13`
`tan theta=(AB)/(BC)=(5k)/(12k)=5/12`
`cosec theta=(AC)/(AB)=(13k)/(5k)=13/5 cot theta=(BC)/(AB)=(12k)/(5k)=12/5` ltrbgt `sin theta=5/13, cos theta=12/13, tan theta=5/12, cosec theta=13/5` and `cot theta =12/5`